Polarkoordinaten potenzieren. z= 2 *(cos (π/3)− i*sin (π/3)). z^3 =?

Question

z= 2 *(cos (π/3)− i*sin (π/3))

Berechnen Sie:

z^3

Bitte mit Rechenschritten.!

Answer 1

z= 2 *(cos (π/3)− i*sin (π/3))

= 2 *(cos (-π/3)+ i*sin (-π/3))

= 2*e^{-iπ/3} 

z^3 = 2^3 * e^ (3* (-iπ/3)) = 8 * e^{-iπ} = -8