Question

If z= 5e^(11pi i/6) what is z^6 in the form a+bi

Answer 1

\[\large z=5e^{11\pi i/6}\]\[z^6=\left(5 e ^{11 \pi i/6}\right)^6=5^6e^{6(11\pi i/6)}=5^6e^{11\pi i}=5^6(\cos 11 \pi + i \sin 11\pi)=-15625+0i\]