Chapter 4, Problem 1PS

(a)

To determine

To calculate: The expression $z^3$ for each of the complex numbers $z=2,z=\frac{-2+2\sqrt{3}i}{2}$ and $z=\frac{-2-2\sqrt{3}i}{2}$. And also, observe the results.

(b)

To determine

To calculate: The expression $z^3$ for each of the complex numbers $z=3,z=\frac{-3+3\sqrt{3}i}{2}$, and $z=\frac{-3-3\sqrt{3}i}{2}$. And also, observe the results.

(c)

To determine

A generalized form for the cube and cube root of a positive real number using the results from part (a) and part (b).