Complex numbers manipulation Find all solutions to $z^4=(z-4)^4$ I have calculated $w^4=\frac{(z-1)^4}{z^4}=1$
then w have the solutions $\pm 1$ and $\pm i $ How do i solve $w=i$ $i=\frac{(z-1)}{z}$ $\rightarrow$ $z-1=iz$ on complex form? Wolfram alpha gives $z=0.5(1+i)$ wich is correct answer

$$
z-1 = iz  \iff (1-i)z = 1 \iff z = \frac{1}{1-i}=\frac{1+i}{(1-i)(1+i)}=\frac{1+i}{2}
$$
