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Ecuación x^2+11=0
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Ecuación x^3-x^2-x-1=0
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Ecuación 5x+12=8x+30
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Ecuación 1/x^2-3/x-4=0
- Expresar {x} en función de y en la ecuación:
- -7*x-13*y=5
- 15*x+1*y=19
- 7*x-1*y=-7
- 20*x+5*y=-3
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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
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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
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Expresiones con funciones
- xy
- xy-1=y-1
- xy+3y-2yx+4x+c
- xy=y-1
- Xy=1+x^(2)
- xy+y=ex,
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
$$x \left(y^{4} + 1\right) + y 2 \left(x y + y\right) = 0$$
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
$$0$$
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 / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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