Finding the fourth roots of $\,5(\cos(3)+i\sin(3)).$

Question

Find the four fourth roots of $\,5(\cos(3)+i\sin(3)).$

I tried to convert to polar form so I could set up an equation like $\,x^4=5e^{i3},\,$ but I am unsure to continue.

Answer 1

We have $$x^4=5e^{i(3+2n\pi)}$$ where $n$ is any integer

$$x=\sqrt[4]5e^{\dfrac{i(3+2n\pi)}4}$$ where $n=0,1,2,3$

Answer 2

Hint: if $x = r \exp i\theta$, then what is the value of $x^4$?