Question

How do you find the `n^{th}` roots of complex numbers in polar form?

Answer 1

`z^(1/n) = r^(1/n) ( cos (theta/n) + i sin(theta/n))`

Explanation:

Polar form of complex number is `z = r( cos theta + i sin theta)`

By De Morvies theorem,

`z^(1/n) = r^(1/n) ( cos (theta/n) + i sin(theta/n))`