\(\displaystyle{ \left(z-1 \right)^4=8 \left(1-i \right)^2}\)
\(\displaystyle{ \left(z-1 \right)^4=-16i}\)
\(\displaystyle{ \left(z-1 \right)^{4}=2^{4} \left(\cos{ \left( - \frac{\pi}{2} \right) }+i\sin{ \left(- \frac{\pi}{2} \right) } \right)}\)
\(\displaystyle{ z-1=2 \left(\cos{ \left( \frac{ \left(4k-1 \right)\pi }{8} \right) }+i\sin{ \left( \frac{ \left(4k-1 \right)\pi }{8} \right) } \right)}\)
\(\displaystyle{ z=2 \left(\cos{ \left( \frac{ \left(4k-1 \right)\pi }{8} \right) }+i\sin{ \left( \frac{ \left(4k-1 \right)\pi }{8} \right) } \right) +1}\)
\(\displaystyle{ k \in \mathbb{Z}_{4}}\)