SOLUTION: Hey, I'm really struggling with this exercise, If |z|=2 and {{{argz=Q}}}, determine the modulus and argument of {{{z^3}}} Thanks!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hey, I'm really struggling with this exercise, If |z|=2 and {{{argz=Q}}}, determine the modulus and argument of {{{z^3}}} Thanks!      Log On


   

Question 542525: Hey, I'm really struggling with this exercise,
If |z|=2 and argz=Q, determine the modulus and argument of z%5E3
Thanks!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You must have been taught that multiplying numbers in polar form is easier, because all you have to do is multiply one modulus times the other and add the arguments.
abs%28z%5E3%29=abs%28z%29%5E3=2%5E3=8 and arg%28z%5E3%29=3%2Aarg%28z%29=3Q%29
If you have not been taught anything about exponents on complex numbers, this problem is a way of introducing de Moivre's formula for the nth power of a complex number.