\(z^{4}=-4 \rightarrow z^{2}=2\sqrt{-1} \rightarrow z=\sqrt{2i}\)
What can you do next?
+118667 Find all complex numbers z such that z^4=-4
It is a power of 4 so there are 4 answers.
first solution
\(z^4=-4\\ z^4=4cis180\\ z=(4cis180)^{1/4}\\ z=\sqrt2(cis(180*\frac{1}{4}))\\ z=\sqrt2(cis(45))\\ z=\sqrt2(1+i)\\ \text{The other solutions will be }\\ z=\sqrt2(-1+i),\quad z=\sqrt2(-1-i)\quad z=\sqrt2(1-i) \)\(\)
