Answer
The power of the complex numbers in the rectangular form is $-4-4\sqrt{3}i$.
Work Step by Step
Here,
$z={{\left[ 2\left( \cos {{80}^{{}^\circ }}+i\sin {{80}^{{}^\circ }} \right) \right]}^{3}}$
Therefore,
$\begin{align}
& z={{\left[ 2\left( \cos {{80}^{{}^\circ }}+i\sin {{80}^{{}^\circ }} \right) \right]}^{3}} \\
& z={{2}^{3}}\left( \cos 3\times {{80}^{{}^\circ }}+i\sin 3\times {{80}^{{}^\circ }} \right) \\
& z=8\left( \cos {{240}^{{}^\circ }}+i\sin {{240}^{{}^\circ }} \right) \\
& z=8\left( -\frac{1}{2}-i\frac{\sqrt{3}}{2} \right) \\
\end{align}$
Simplify it further, to get,
$z=-4-4\sqrt{3}i$
The power of the complex number in the rectangular form is $z=-4-4\sqrt{3}i$
