Answer
The power of the complex numbers in the rectangular form is $\frac{i}{64}$.
Work Step by Step
Here,
$z={{\left[ \frac{1}{2}\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right) \right]}^{6}}$ (I)
Therefore
$\begin{align}
& z={{\left[ \frac{1}{2}\left( \cos \frac{\pi }{12}+i\sin \frac{\pi }{12} \right) \right]}^{6}} \\
& z=\frac{1}{{{2}^{6}}}\left( \cos 6\times \frac{\pi }{12}+i\sin 6\times \frac{\pi }{12} \right) \\
& z=\frac{1}{64}\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right) \\
& z=\frac{1}{64}\left( 0+i \right) \\
\end{align}$
Simplify it further, to get,
$z=\frac{i}{64}$
The complex number in the rectangular form is $z=\frac{i}{64}$
