Potęga liczby zespolonej

[tepa_dzida]

\(\displaystyle{ z=i-1}\)

\(\displaystyle{ z=(i-1)^{2004}}\)

\(\displaystyle{ |z|= \sqrt{2}}\)

\(\displaystyle{ \phi = \frac{ \pi }{4}}\)

\(\displaystyle{ z^{2004}=2^{1002}(cos 2004* \frac{ \pi }{4} + i*sin 2004*\frac{ \pi }{4})}\)

\(\displaystyle{ z^{2004}=2^{1002}(cos501 \pi +i*sin501 \pi)}\)

Co dalej?

[irena_1]

\(\displaystyle{ cos501\pi=cos\pi=-1\\sin501\pi=sin\pi=0}\)