Express $z$ where $z=\frac{10-2\sqrt{3}\mathbf{i}}{1-3\sqrt{3}\mathbf{i}}$ in the form \(x+

Question

Express $z$ where $z=\frac{10-2\sqrt{3}\mathbf{i}}{1-3\sqrt{3}\mathbf{i}}$ in the form $x+y\mathbf{i}$, where $x$ and $y$ are real. Without the use of a G.C., prove that ${{z}^{21}}$ is a real number.

Accepted Answer

$1+\sqrt{3}\mathbf{i}$

Complex Numbers - Complex Numbers - General

Complex Numbers - Complex Numbers - General