complex numbers investigation task

Investigate the solutions of the equations of the form $z^n=2^n$, $n\in \mathbb{N}$.

For example $z^1=2^1$, $z^2=2^2$, $z^3=2^3$, etc.

As part of your investigation:

• determine the solutions when n=1,2,3,4…
• plot solutions of the equations in Argand diagrams
• represent some of the solutions in Cartesian form and some in polar form, whatever is most appropriate
• look for patterns in the solutions depending on the values of n, such as how many solutions there are, the angle between the solutions etc.
• summarize your findings in a final paragraph

You may use CAS but show working out.