Math Problem Solver

Roots

\[\sqrt{\frac{54 \cdot {a}^{-4}}{6 a}} = i \left(- 3 \sqrt[4]{\frac{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)}\right) - 3 \sqrt[4]{\frac{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)} \approx - 0.948683298050514 i \left(\frac{\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- 0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} + \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)} - 0.948683298050514 \left(\frac{\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- 0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} + \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)}\]\[\sqrt{\frac{54 \cdot {a}^{-4}}{6 a}} = i 3 \sqrt[4]{\frac{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)} + 3 \sqrt[4]{\frac{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)} \approx 0.948683298050514 i \left(\frac{\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- 0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} + \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)} + 0.948683298050514 \left(\frac{\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}} + \frac{\left(- 0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} + \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}}{\left(\left(- 0.5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - 0.1 \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(0.1 \left(\operatorname{re}{\left(a\right)}\right)^{5} - \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 0.5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}\right)^{2}}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(\frac{- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}},- \frac{- \left(\operatorname{re}{\left(a\right)}\right)^{5} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} - 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}}{\left(- 5 \left(\operatorname{re}{\left(a\right)}\right)^{4} \operatorname{im}{\left(a\right)} + 10 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{3} - \left(\operatorname{im}{\left(a\right)}\right)^{5}\right)^{2} + \left(\left(\operatorname{re}{\left(a\right)}\right)^{5} - 10 \left(\operatorname{re}{\left(a\right)}\right)^{3} \left(\operatorname{im}{\left(a\right)}\right)^{2} + 5 \operatorname{re}{\left(a\right)} \left(\operatorname{im}{\left(a\right)}\right)^{4}\right)^{2}} \right)}}{2} \right)}\]