Find all complex numbers z such that z^4 = -4.
Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.
I have an idea of how to solve this but I just want to see how others would solve it. Thanks!
\(z^4 = -4 = 4e^{i(2k+1)\pi},~k\in \mathbb{Z}\\ z = \sqrt{2}e^{i(2k+1)\pi/4},~k=0,1,2,3\\ z = 1+i,~-1+i,~-1-i,~1-i\)
Thanks.
