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- La ecuación:
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Ecuación x^2+5x=36
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Ecuación 9-7(x+3)=5-6x
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Ecuación 4x-5=3+2(x+1)
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Ecuación 6/(x-2)+5/x=3
- Expresar {x} en función de y en la ecuación:
- -14*x-12*y=-13
- -20*x+14*y=16
- -7*x+15*y=-11
- -14*x+5*y=3
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Expresiones idénticas
- cuatro sqtr(x)-(a+ cinco)2sqrt(x)+4a+4= cero
- 4sqtr(x) menos (a más 5)2 raíz cuadrada de (x) más 4a más 4 es igual a 0
- cuatro sqtr(x) menos (a más cinco)2 raíz cuadrada de (x) más 4a más 4 es igual a cero
- 4sqtr(x)-(a+5)2√(x)+4a+4=0
- 4sqtrx-a+52sqrtx+4a+4=0
- 4sqtr(x)-(a+5)2sqrt(x)+4a+4=O
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Expresiones semejantes
- 4sqtr(x)-(a-5)2sqrt(x)+4a+4=0
- 4sqtr(x)+(a+5)2sqrt(x)+4a+4=0
- 4sqtr(x)-(a+5)2sqrt(x)-4a+4=0
- 4sqtr(x)-(a+5)2sqrt(x)+4a-4=0
4sqtr(x)-(a+5)2sqrt(x)+4a+4=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
___ ___ 4*\/ x - (a + 5)*2*\/ x + 4*a + 4 = 0
$$\left(4 a + \left(- \sqrt{x} 2 \left(a + 5\right) + 4 \sqrt{x}\right)\right) + 4 = 0$$
Gráfica
Respuesta rápida
[src]
/ _________________ / _________________ \ _________________ / _________________ \ \ / _________________ \ / _________________ \ _________________
| 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ | | 4 / 2 2 /atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\
| \/ im (x) + re (x) *|2 - 3*\/ im (x) + re (x) *cos|-------------------||*sin|-------------------| 3*\/ im (x) + re (x) *|-2 + \/ im (x) + re (x) *cos|-------------------||*sin|-------------------| | |-2 + \/ im (x) + re (x) *cos|-------------------||*|2 - 3*\/ im (x) + re (x) *cos|-------------------|| 3*\/ im (x) + re (x) *sin |-------------------|
| \ \ 2 // \ 2 / \ \ 2 // \ 2 / | \ \ 2 // \ \ 2 // \ 2 /
a1 = I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------
| 2 2 | 2 2
| / _________________ \ _________________ / _________________ \ _________________ | / _________________ \ _________________ / _________________ \ _________________
| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\
| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------|| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------|
\ \ \ 2 // \ 2 / \ \ 2 // \ 2 // \ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$a_{1} = \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
a1 = (-3*(re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x, re(x))/2) + 2)*((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2) + i*(-(-3*(re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) + 2)*(re(x)^2 + im(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2) - 3*((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)*(re(x)^2 + im(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2)/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2)) - 3*sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2/(((re(x)^2 + im(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) - 2)^2 + sqrt(re(x)^2 + im(x)^2)*sin(atan2(im(x), re(x))/2)^2))
Suma y producto de raíces
[src]
suma
/ _________________ / _________________ \ _________________ / _________________ \ \ / _________________ \ / _________________ \ _________________ | 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ | | 4 / 2 2 /atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | \/ im (x) + re (x) *|2 - 3*\/ im (x) + re (x) *cos|-------------------||*sin|-------------------| 3*\/ im (x) + re (x) *|-2 + \/ im (x) + re (x) *cos|-------------------||*sin|-------------------| | |-2 + \/ im (x) + re (x) *cos|-------------------||*|2 - 3*\/ im (x) + re (x) *cos|-------------------|| 3*\/ im (x) + re (x) *sin |-------------------| | \ \ 2 // \ 2 / \ \ 2 // \ 2 / | \ \ 2 // \ \ 2 // \ 2 / I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------ | 2 2 | 2 2 | / _________________ \ _________________ / _________________ \ _________________ | / _________________ \ _________________ / _________________ \ _________________ | | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------|| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| \ \ \ 2 // \ 2 / \ \ 2 // \ 2 // \ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
=
/ _________________ / _________________ \ _________________ / _________________ \ \ / _________________ \ / _________________ \ _________________ | 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ | | 4 / 2 2 /atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | \/ im (x) + re (x) *|2 - 3*\/ im (x) + re (x) *cos|-------------------||*sin|-------------------| 3*\/ im (x) + re (x) *|-2 + \/ im (x) + re (x) *cos|-------------------||*sin|-------------------| | |-2 + \/ im (x) + re (x) *cos|-------------------||*|2 - 3*\/ im (x) + re (x) *cos|-------------------|| 3*\/ im (x) + re (x) *sin |-------------------| | \ \ 2 // \ 2 / \ \ 2 // \ 2 / | \ \ 2 // \ \ 2 // \ 2 / I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------ | 2 2 | 2 2 | / _________________ \ _________________ / _________________ \ _________________ | / _________________ \ _________________ / _________________ \ _________________ | | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------|| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| \ \ \ 2 // \ 2 / \ \ 2 // \ 2 // \ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
producto
/ _________________ / _________________ \ _________________ / _________________ \ \ / _________________ \ / _________________ \ _________________ | 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ 4 / 2 2 | 4 / 2 2 /atan2(im(x), re(x))\| /atan2(im(x), re(x))\ | | 4 / 2 2 /atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | \/ im (x) + re (x) *|2 - 3*\/ im (x) + re (x) *cos|-------------------||*sin|-------------------| 3*\/ im (x) + re (x) *|-2 + \/ im (x) + re (x) *cos|-------------------||*sin|-------------------| | |-2 + \/ im (x) + re (x) *cos|-------------------||*|2 - 3*\/ im (x) + re (x) *cos|-------------------|| 3*\/ im (x) + re (x) *sin |-------------------| | \ \ 2 // \ 2 / \ \ 2 // \ 2 / | \ \ 2 // \ \ 2 // \ 2 / I*|- ------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------ | 2 2 | 2 2 | / _________________ \ _________________ / _________________ \ _________________ | / _________________ \ _________________ / _________________ \ _________________ | | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\| | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | 4 / 2 2 /atan2(im(x), re(x))\| / 2 2 2/atan2(im(x), re(x))\ | |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------|| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| |-2 + \/ im (x) + re (x) *cos|-------------------|| + \/ im (x) + re (x) *sin |-------------------| \ \ \ 2 // \ 2 / \ \ 2 // \ 2 // \ \ 2 // \ 2 / \ \ 2 // \ 2 /
$$\frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} + i \left(- \frac{\left(- 3 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}} - \frac{3 \left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right) \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}\right) - \frac{3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}{\left(\sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 2\right)^{2} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)}}$$
=
_________________ _________________ _________________
/ 2 2 4 / 2 2 /atan2(im(x), re(x))\ 4 / 2 2 /atan2(im(x), re(x))\
-4 - 3*\/ im (x) + re (x) + 8*\/ im (x) + re (x) *cos|-------------------| + 4*I*\/ im (x) + re (x) *sin|-------------------|
\ 2 / \ 2 /
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_________________ _________________
/ 2 2 4 / 2 2 /atan2(im(x), re(x))\
4 + \/ im (x) + re (x) - 4*\/ im (x) + re (x) *cos|-------------------|
\ 2 /
$$\frac{4 i \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + 8 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} - 3 \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} - 4}{- 4 \sqrt[4]{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\operatorname{im}{\left(x\right)},\operatorname{re}{\left(x\right)} \right)}}{2} \right)} + \sqrt{\left(\operatorname{re}{\left(x\right)}\right)^{2} + \left(\operatorname{im}{\left(x\right)}\right)^{2}} + 4}$$
(-4 - 3*sqrt(im(x)^2 + re(x)^2) + 8*(im(x)^2 + re(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2) + 4*i*(im(x)^2 + re(x)^2)^(1/4)*sin(atan2(im(x), re(x))/2))/(4 + sqrt(im(x)^2 + re(x)^2) - 4*(im(x)^2 + re(x)^2)^(1/4)*cos(atan2(im(x), re(x))/2))