Matemática, perguntado por babilica2589, 9 meses atrás

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

Soluções para a tarefa

Respondido por alice82576
0

\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}

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