Question

Find all solutions for the following complex number: z^4 /4=1

Answer 1

z^4-4 =0

(z^2+2)(z^2-2)=0
(z+isqrt2)(z-isqrt2)(z+sqrt2)(z-sqrt2)=0

so you have four roots.

Now there is another way to do this in your head. Using de Morives theorem, in polar form

z^4=4=4@n360deg n=0,1,2,3
z=sqrt2 @ n*90
which translates on the complex plane as the same roots above.