Question

Exercițiul din poză
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Answer 1

$\frac{1}{2}+i\frac{\sqrt{3}}{2}=e^{i\frac{\pi}{3}}$

$\frac{1}{2}-i\frac{1}{2}=e^{-i\frac{\pi}{4}}$

Deci

$\left(\dfrac{\frac{1}{2}+i\frac{\sqrt{3}}{2}}{\frac{1}{2}-i\frac{1}{2}}\right)^{40}=\left(e^{i\frac{\pi}{3}}e^{i\frac{\pi}{4}}\right)^{40}=e^{i\frac{40\pi}{3}}e^{i10\pi}=e^{i(13\pi+\frac{\pi}{3})}=-e^{i\frac{\pi}{3}}=-\frac{1}{2}-i\frac{\sqrt{3}}{2}.$