Roots of a fourth order polynomial

Question

I am looking for the roots of $x^4=-1$, I have written $ -1 $ using Euler as $e^{j180}$. Therefore, $x=\pm e^{j45}$. But the fourth order equation should have two other roots, how can I get them?

Answer 1

You can write it as $x^4=i^2$ thus $(x-i^{0.5})(x+i^{0.5})(x^2+i)=0$ can you get $4$ roots now.