Im trying find all solutions for:
Should I convert z into or if I want to interpret my result geometrically?
What I have done so far is:
Not sure what to do with my results. I'm a little lost with the general values for z; I am fine with the definite values such as etc. Not sure which direction to head to solve for this equation so I can interpret geometrically.
Take absolute values of both sides of , getting , so |z|=0 or |z|=1. Since 0 is easily seen to be a solution, we're focused on possible solutions on the unit circle.
Now multiply your original equation by z, getting . Do you know an identity relating and |z|? This should lead you to consider cube roots of unity, which have a nice geometric interpretation. You might get some extraneous solutions here though (possibly, too tired to trust myself now lol).