Question

Evaluate the expression
`\sqrt[5]{3125{e}^{(11 \pi )/(2) i}}`, leaving your answer in polar form.

Answer 1

`\sqrt[5]{3125e^{(11\pi)/(2)i}}\\=\\\sqrt[5]{3125}\sqrt[5]{e^{(11\pi)/(2)}i}\\\\=5e^{(11\pi)/(10)i}\\\\\boxed{5\left(\cos \left((11\pi)/(10) \right)+i \sin \left((11\pi)/(10) \right) \right)}`