Question

find all the nth roots of z. leave in polar form
81e^60i n=4

Answer 1

\[\Large\rm z=81e^{60\mathcal i}\]Is 60 in degrees?
I'll assume that it is for now I guess.\[\Large\rm z=81e^{\frac{\pi}{3}\mathcal i}\]We can work with it in radians much easier.
The thing to realize, and this is what allows us to find `multiple roots`, is that...
The 81 is telling us to go out in the real direction a distance of 81,

Answer 2

While the `Argument` of the exponential is telling us how far to rotate.

Answer 3

If we were to ADD 2pi to our angle, we would end up at the same location, yes?\[\Large\rm z=81e^{\mathcal i\left(\frac{\pi}{3}+2\pi\right)}\]