Roots of Complex Number/Corollary/Examples/Cube Roots of 8i

Example of Roots of Complex Number: Corollary
The complex $4$th roots of $8 i$ are given by:
 * $\paren {2 - 2 i}^{1/4} = \set {2 i, \sqrt 3 + i, -\sqrt 3 + i}$

Proof
Let $z = 8 i$.

Then:
 * $z = 8 \exp \paren {\dfrac {i \pi} 2}$

Let $b$ be defined as:

Then we have that the complex cube roots of unity are:
 * $1, \exp {\dfrac {2 i \pi} 3}, \exp {\dfrac {-2 i \pi} 3}$

Thus from Roots of Complex Number: Corollary: