Question

calcular z^17, sabendo que z=cos π/4+i.sen π/4​

Answer 1

$\left(\cos\left(\dfrac{\pi}{4}\right)+i\sin\left(\dfrac{\pi}{4}\right)\right)^{17}=\\\\\\(e^{\frac{\pi i}{4}})^{17}=\\\\\\e^{\frac{17\pi i}{4}}=\\\\\\\cos\left(\dfrac{17\pi}{4}\right)+i\sin\left(\dfrac{17\pi}{4}\right)=\\\\\\\dfrac{\sqrt2}{2}+i\dfrac{\sqrt2}{2}$