Hallo,
z^3=-27 hat drei Lösungen.
In Polarform:
\((r\cdot e^{i\varphi})^3=27 \cdot e^{i\pi}\)
\(r^3\cdot e^{i\cdot3\varphi}=27 \cdot e^{i\pi}\)
\(r^3=27\Rightarrow r=3\)
\(3\varphi_n=\pi +n\cdot 2\pi~~~;~~~n\in\Z\)
Also:
\(\varphi_0=\pi/3\)
\(\varphi_1=(2\pi+\pi)/3=\pi\)
\(\varphi_2=(4\pi+\pi)/3=5\pi/3\)
:-)
PS:
\(\varphi_4=\varphi_0\) usw.
