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)`

![https://www.google.com/search?q=demorvies+theorem&client=safari&hl=en-us&prmd=ivn&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiYmuTisNLbAhWJwI8KHXycAGsQ_AUIESgB&biw=768&bih=922#imgrc=XMEZvta0Lgq8wM:]()

By De Morvies theorem,

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