Bardzo proszę o sprawdzenie
\(\displaystyle{ (-\sqrt{3}+i)^{23}}\)
\(\displaystyle{ z=-\sqrt{3}+i}\)
\(\displaystyle{ \left|z\right|=2}\)
\(\displaystyle{ \cos \varphi=- \frac{ \sqrt{3} }{2}}\)
\(\displaystyle{ \sin \varphi= \frac{1}{2}}\)
\(\displaystyle{ \varphi=\pi- \frac{\pi}{6} = \frac{5}{6}\pi}\)
\(\displaystyle{ z^{n}= \left| z\right|^{n}(\cos n \varphi+ i sin n \varphi)}\)
\(\displaystyle{ z^{23}= 2^{23}(cos \frac{115}{6}\pi + i sin \frac{115}{6}\pi)}\)
\(\displaystyle{ z^{23}= 2^{23}(cos \frac{7}{6}\pi + i sin \frac{7}{6}\pi)}\)
\(\displaystyle{ z^{23}= 2^{23}(-cos \frac{\pi}{6} - i sin \frac{\pi}{6})}\)
\(\displaystyle{ z^{23}= 2^{23}(- \frac{ \sqrt{3} }{2} - \frac{1}{2} i)}\)
\(\displaystyle{ z^{23}= 2^{22}(- \sqrt{3} - i)}\)
