If z=(3/5)-(4/5)i , what is z^10 and the three cube roots of z

Question

This is a polar coordinate and complex numbers question. (powers of complex numbers)

Answer 1

Convert to polar notation

r²= (3/5)² + (4/5)² = 1

θ = arctan(4/3)

Now use DeMoivre's theorem to get you answers.

Fortunately since r is 1, there is no real trouble calculating the roots of r and the arguments will be found by division!