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La ecuación:
Ecuación 3^x=27
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
Ecuación x(x^2+2x+1)=6(x+1)
Ecuación 4x+1=-3x+15
Expresar {x} en función de y en la ecuación:
-6*x-20*y=8
7*x-1*y=0
2*x-8*y=4
2*x-15*y=-1
Expresiones idénticas
dos (xy+y)y+x(y^ cuatro + uno)= cero
2(xy más y)y más x(y en el grado 4 más 1) es igual a 0
dos (xy más y)y más x(y en el grado cuatro más uno) es igual a cero
2(xy+y)y+x(y4+1)=0
2xy+yy+xy4+1=0
2(xy+y)y+x(y⁴+1)=0
2xy+yy+xy^4+1=0
2(xy+y)y+x(y^4+1)=O
Expresiones semejantes
2(xy+y)y+x(y^4-1)=0
2(xy+y)y-x(y^4+1)=0
2(xy-y)y+x(y^4+1)=0
Expresiones con funciones
xy
Xy=1+x^(2)
xy+y=ex,
xy-7x-(x-4xy)=0
xy-y=x^2cosx
xyy=lnx

2(xy+y)y+x(y^4+1)=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

                  / 4    \    
2*(x*y + y)*y + x*\y  + 1/ = 0

x \left(y^{4} + 1\right) + y 2 \left(x y + y\right) = 0

Simplificar

Gráfica

Respuesta rápida [src]

                                                                                                      /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\
              ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||
             /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||
            /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||
           /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|
y1 = -    /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| - I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------|
       4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /
       \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/

y_{1} = - i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}

                                                                                                    /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\
            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||
           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||
          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||
         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|
y2 =    /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| + I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------|
     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /
     \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/

y_{2} = i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}

                                                                                                    /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\
              __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||
             /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
            /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||
           /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|
y3 = -    /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| - I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------|
       4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /
       \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /

y_{3} = - i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}

                                                                                                  /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\
            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||
           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||
         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|
y4 =    /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| + I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------|
     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /
     \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /

y_{4} = i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}

y4 = i*((im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2))^2 + (re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))^2)^(1/4)*sin(atan2(im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2, re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))/2) + ((im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2))^2 + (re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))^2)^(1/4)*cos(atan2(im(sqrt(2*x + 1)/x) + im(x)/(re(x)^2 + im(x)^2), re(sqrt(2*x + 1)/x) - 1 - re(x)/(re(x)^2 + im(x)^2))/2))

Suma y producto de raíces [src]

suma

                                                                                                 /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\                                                                                                  /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\                                                                                                  /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\                                                                                                /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\
         ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||          ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||          __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||
        /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||         /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||         /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||
       /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||        /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||        /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||
      /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|       /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|       /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|
-    /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| - I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------| +    /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| + I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------| + -    /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| - I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------| +    /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| + I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------|
  4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /   4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /   4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /
  \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                             \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                           \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /

\left(i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(\left(- i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(\left(- i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) + \left(i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right)\right)\right)

0

producto

/                                                                                                 /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\\ /                                                                                               /     /    /  _________\                           /  _________\                  \\                                                                                                    /     /    /  _________\                           /  _________\                  \\\ /                                                                                               /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\\ /                                                                                             /     /                    /  _________\                           /  _________\\\                                                                                                  /     /                    /  _________\                           /  _________\\\\
|         ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||| |       ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||            ____________________________________________________________________________________    |     |    |\/ 1 + 2*x |        im(x)              |\/ 1 + 2*x |        re(x)     ||| |         __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||| |       __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x |||            __________________________________________________________________________________    |     |     im(x)          |\/ 1 + 2*x |            re(x)          |\/ 1 + 2*x ||||
|        /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||| |      /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||           /                                      2                                           2     |atan2|- im|-----------| + ---------------, -1 - re|-----------| - ---------------||| |        /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||| |      /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------|||           /                                    2                                           2     |atan2|--------------- + im|-----------|, -1 - --------------- + re|-----------||||
|       /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||| |     /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||          /  /    /  _________\                  \    /       /  _________\                  \      |     |    \     x     /     2        2            \     x     /     2        2   ||| |       /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||| |     /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /||          /  /                    /  _________\\    /                         /  _________\\      |     |  2        2        \     x     /         2        2        \     x     /|||
|      /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|| |    /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|         /   |    |\/ 1 + 2*x |        im(x)     |    |       |\/ 1 + 2*x |        re(x)     |      |     \                    im (x) + re (x)                         im (x) + re (x)/|| |      /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|| |    /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /|         /   |     im(x)          |\/ 1 + 2*x ||    |          re(x)          |\/ 1 + 2*x ||      |     \im (x) + re (x)                         im (x) + re (x)                  /||
|-    /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| - I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------||*|   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *cos|----------------------------------------------------------------------------------| + I*   /    |- im|-----------| + ---------------|  + |-1 - re|-----------| - ---------------|  *sin|----------------------------------------------------------------------------------||*|-    /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| - I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------||*|   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *cos|--------------------------------------------------------------------------------| + I*   /    |--------------- + im|-----------||  + |-1 - --------------- + re|-----------||  *sin|--------------------------------------------------------------------------------||
|  4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /| |4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /     4 /     |    \     x     /     2        2   |    |       \     x     /     2        2   |      \                                        2                                         /| |  4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /| |4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /     4 /     |  2        2        \     x     /|    |       2        2        \     x     /|      \                                       2                                        /|
\  \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                          / \\/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                               \/      \                    im (x) + re (x)/    \                       im (x) + re (x)/                                                                                          / \  \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                        / \\/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                             \/      \im (x) + re (x)                  /    \     im (x) + re (x)                  /                                                                                        /

\left(- i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},- \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(- i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} - \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right) \left(i \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)} + \sqrt[4]{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2} + \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \frac{\operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1 - \frac{\operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}{2} \right)}\right)

                                                                                                                                                                                                                             /                    /  _________\                   /       /  _________\\                  \          /                      /  _________\                   /      /  _________\\                  \
                                                                                                                                                                                                                             |/  2        2   \   |\/ 1 + 2*x |                   |       |\/ 1 + 2*x || /  2        2   \|          |  /  2        2   \   |\/ 1 + 2*x |                   |      |\/ 1 + 2*x || /  2        2   \|
                                                                                                                                                                                                                             |\im (x) + re (x)/*im|-----------| + im(x)  -re(x) + |-1 + re|-----------||*\im (x) + re (x)/|          |- \im (x) + re (x)/*im|-----------| + im(x)  -re(x) - |1 + re|-----------||*\im (x) + re (x)/|
      ____________________________________________________________________________________________________       ___________________________________________________________________________________________________         |                    \     x     /                   \       \     x     //                  |          |                      \     x     /                   \      \     x     //                  |
     /                                             2                                                    2       /                                                  2                                              2   I*atan2|-----------------------------------------, -------------------------------------------------| + I*atan2|-------------------------------------------, ------------------------------------------------|
    /  /                             /  _________\\    //      /  _________\\                          \       /  //      /  _________\\                          \    /                    /  _________\        \           |               2        2                                     2        2                    |          |                2        2                                     2        2                    |
   /   |         /  2        2   \   |\/ 1 + 2*x ||    ||      |\/ 1 + 2*x || /  2        2   \        |      /   ||      |\/ 1 + 2*x || /  2        2   \        |    |/  2        2   \   |\/ 1 + 2*x |        |           \             im (x) + re (x)                                im (x) + re (x)                 /          \              im (x) + re (x)                                im (x) + re (x)                 /
  /    |-im(x) + \im (x) + re (x)/*im|-----------||  + ||1 + re|-----------||*\im (x) + re (x)/ + re(x)|  *  /    ||1 - re|-----------||*\im (x) + re (x)/ + re(x)|  + |\im (x) + re (x)/*im|-----------| + im(x)|  *e                                                                                                                                                                                                              
\/     \                             \     x     //    \\      \     x     //                          /   \/     \\      \     x     //                          /    \                    \     x     /        /                                                                                                                                                                                                                  
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                                                                                                                                                                                                                          2                                                                                                                                                                                                         
                                                                                                                                                                                                         /  2        2   \                                                                                                                                                                                                          
                                                                                                                                                                                                         \im (x) + re (x)/

\frac{\sqrt{\left(\left(1 - \operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)}\right) \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) + \operatorname{re}{\left(x\right)}\right)^{2} + \left(\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \operatorname{im}{\left(x\right)}\right)^{2}} \sqrt{\left(\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + 1\right) + \operatorname{re}{\left(x\right)}\right)^{2} + \left(\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - \operatorname{im}{\left(x\right)}\right)^{2}} e^{i \operatorname{atan_{2}}{\left(\frac{- \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{- \left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + 1\right) - \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)} + i \operatorname{atan_{2}}{\left(\frac{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \operatorname{im}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} + \operatorname{im}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}},\frac{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right) \left(\operatorname{re}{\left(\frac{\sqrt{2 x + 1}}{x}\right)} - 1\right) - \operatorname{re}{\left(x\right)}}{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \right)}}}{\left(\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}\right)^{2}}

sqrt((-im(x) + (im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x))^2 + ((1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2) + re(x))^2)*sqrt(((1 - re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2) + re(x))^2 + ((im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))^2)*exp(i*atan2(((im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))/(im(x)^2 + re(x)^2), (-re(x) + (-1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2))/(im(x)^2 + re(x)^2)) + i*atan2((-(im(x)^2 + re(x)^2)*im(sqrt(1 + 2*x)/x) + im(x))/(im(x)^2 + re(x)^2), (-re(x) - (1 + re(sqrt(1 + 2*x)/x))*(im(x)^2 + re(x)^2))/(im(x)^2 + re(x)^2)))/(im(x)^2 + re(x)^2)^2

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