z^5-4z=0 \\ \Rightarrow z(z^4-4)=0 \\ \Rightarrow z(z^2-2)(z^2+2)=0 \\\Rightarrow z(z+\sqrt{2})(z-\sqrt{2}) (z+\sqrt{2}i)(z-\sqrt{2}i)=0 \\ z=0, \pm \sqrt{2}, \pm \sqrt{2}i\\ \\ \\ $another way to solve $ z^4=4: \\ z=\sqrt[\frac{1}{4}]{4} \\= \left ( 4cis( 2n \pi) \right )^{\frac{1}{4}} \\ =...