Sr Examen

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x=(-1*((13*y^2)/(y+5)*(y-5)))^1/2 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

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Solución numérica:

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Solución

Ha introducido [src] 
         _________________
        /       2         
       /    13*y          
x =   /   - -----*(y - 5) 
    \/      y + 5
x=−13y2y+5(y−5)x = \sqrt{- \frac{13 y^{2}}{y + 5} \left(y - 5\right)}
Simplificar
Solución detallada
Tenemos la ecuación:
x=−13y2y+5(y−5)x = \sqrt{- \frac{13 y^{2}}{y + 5} \left(y - 5\right)}
cambiamos:
x=13y2(5−y)y+5x = \sqrt{13} \sqrt{\frac{y^{2} \left(5 - y\right)}{y + 5}}
Abrimos los paréntesis en el miembro derecho de la ecuación
x = sqrt13sqrty+2*+5+y5+y)

Sumamos los términos semejantes en el miembro derecho de la ecuación:
x = sqrt(13)*sqrt(y^2*(5 - y)/(5 + y))

Obtenemos la respuesta: x = sqrt(13)*sqrt(y^2*(5 - y)/(5 + y))
Gráfica
Respuesta rápida [src] 
                  _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\                  _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\
                 /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||                 /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||
                /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||                /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||
       ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|       ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|
x1 = \/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *cos|---------------------------------------------------------------------------------------| + I*\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *sin|---------------------------------------------------------------------------------------|
            \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /            \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /
x1=13i((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24sin⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)+13((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24cos⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)x_{1} = \sqrt{13} i \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} + \sqrt{13} \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} 
x1 = sqrt(13)*i*(((5 - re(y))*re(y^2/(y + 5)) + im(y)*im(y^2/(y + 5)))^2 + ((5 - re(y))*im(y^2/(y + 5)) - re(y^2/(y + 5))*im(y))^2)^(1/4)*sin(atan2((5 - re(y))*im(y^2/(y + 5)) - re(y^2/(y + 5))*im(y, (5 - re(y))*re(y^2/(y + 5)) + im(y)*im(y^2/(y + 5)))/2) + sqrt(13)*(((5 - re(y))*re(y^2/(y + 5)) + im(y)*im(y^2/(y + 5)))^2 + ((5 - re(y))*im(y^2/(y + 5)) - re(y^2/(y + 5))*im(y))^2)^(1/4)*cos(atan2((5 - re(y))*im(y^2/(y + 5)) - re(y^2/(y + 5))*im(y), (5 - re(y))*re(y^2/(y + 5)) + im(y)*im(y^2/(y + 5)))/2))
Suma y producto de raíces [src] 
suma
             _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\                  _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\
            /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||                 /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||
           /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||                /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||
  ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|       ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|
\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *cos|---------------------------------------------------------------------------------------| + I*\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *sin|---------------------------------------------------------------------------------------|
       \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /            \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /
13i((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24sin⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)+13((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24cos⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)\sqrt{13} i \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} + \sqrt{13} \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} 
=
             _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\                  _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\
            /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||                 /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||
           /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||                /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||
  ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|       ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|
\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *cos|---------------------------------------------------------------------------------------| + I*\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *sin|---------------------------------------------------------------------------------------|
       \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /            \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /
13i((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24sin⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)+13((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24cos⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)\sqrt{13} i \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} + \sqrt{13} \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} 
producto
             _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\                  _________________________________________________________________________________________    /     /              /   2 \           /   2 \                /   2 \           /   2 \\\
            /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||                 /                                          2                                            2     |     |              |  y  |           |  y  |                |  y  |           |  y  |||
           /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||                /  /              /   2 \           /   2 \\    /              /   2 \           /   2 \\      |atan2|(5 - re(y))*im|-----| - im(y)*re|-----|, (5 - re(y))*re|-----| + im(y)*im|-----|||
  ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|       ____    /   |              |  y  |           |  y  ||    |              |  y  |           |  y  ||      |     \              \5 + y/           \5 + y/                \5 + y/           \5 + y//|
\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *cos|---------------------------------------------------------------------------------------| + I*\/ 13 *4 /    |(5 - re(y))*im|-----| - im(y)*re|-----||  + |(5 - re(y))*re|-----| + im(y)*im|-----||  *sin|---------------------------------------------------------------------------------------|
       \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /            \/     \              \5 + y/           \5 + y//    \              \5 + y/           \5 + y//      \                                           2                                           /
13i((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24sin⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)+13((5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2+((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y))24cos⁡(atan2⁡((5−re⁡(y))im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),(5−re⁡(y))re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2)\sqrt{13} i \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} + \sqrt{13} \sqrt[4]{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},\left(5 - \operatorname{re}{\left(y\right)}\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2} \right)} 
=
                                                                                                                 /                 /   2 \           /   2 \          /   2 \                  /   2 \\
                                                                                                                 |                 |  y  |           |  y  |          |  y  |                  |  y  ||
             ___________________________________________________________________________________________  I*atan2|- (-5 + re(y))*im|-----| - im(y)*re|-----|, im(y)*im|-----| - (-5 + re(y))*re|-----||
            /                                           2                                             2          \                 \5 + y/           \5 + y/          \5 + y/                  \5 + y//
           /  /               /   2 \           /   2 \\    /               /   2 \           /   2 \\    ---------------------------------------------------------------------------------------------
  ____    /   |               |  y  |           |  y  ||    |               |  y  |           |  y  ||                                                  2                                              
\/ 13 *4 /    |(-5 + re(y))*im|-----| + im(y)*re|-----||  + |(-5 + re(y))*re|-----| - im(y)*im|-----||  *e                                                                                             
       \/     \               \5 + y/           \5 + y//    \               \5 + y/           \5 + y//
13((re⁡(y)−5)re⁡(y2y+5)−im⁡(y)im⁡(y2y+5))2+((re⁡(y)−5)im⁡(y2y+5)+re⁡(y2y+5)im⁡(y))24eiatan2⁡(−(re⁡(y)−5)im⁡(y2y+5)−re⁡(y2y+5)im⁡(y),−(re⁡(y)−5)re⁡(y2y+5)+im⁡(y)im⁡(y2y+5))2\sqrt{13} \sqrt[4]{\left(\left(\operatorname{re}{\left(y\right)} - 5\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)}\right)^{2} + \left(\left(\operatorname{re}{\left(y\right)} - 5\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)}\right)^{2}} e^{\frac{i \operatorname{atan_{2}}{\left(- \left(\operatorname{re}{\left(y\right)} - 5\right) \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} - \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} \operatorname{im}{\left(y\right)},- \left(\operatorname{re}{\left(y\right)} - 5\right) \operatorname{re}{\left(\frac{y^{2}}{y + 5}\right)} + \operatorname{im}{\left(y\right)} \operatorname{im}{\left(\frac{y^{2}}{y + 5}\right)} \right)}}{2}} 
sqrt(13)*(((-5 + re(y))*im(y^2/(5 + y)) + im(y)*re(y^2/(5 + y)))^2 + ((-5 + re(y))*re(y^2/(5 + y)) - im(y)*im(y^2/(5 + y)))^2)^(1/4)*exp(i*atan2(-(-5 + re(y))*im(y^2/(5 + y)) - im(y)*re(y^2/(5 + y)), im(y)*im(y^2/(5 + y)) - (-5 + re(y))*re(y^2/(5 + y)))/2)
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