Roots of Complex Number/Examples/Cube Roots of 8

Example of Roots of Complex Number
The complex cube roots of $8$ are given by:
 * $\paren 8^{1/3} = \set {2 \, \map \cis {120 k} \degrees}$

for $k = 0, 1, 2$.

That is:

Proof

 * Complex Cube Roots of 8.png

Let $z^3 = 8$.

We have that:
 * $z^3 = 8 \, \map \cis {0 + 2 k \pi}$

Let $z = r \cis \theta$.

Then: