I'm not 100% sure of the solution to the following problem:
Find all the solutions of:
, where z=x+iy
I attempted doing this question the way my lecture notes seem to indicate, as follows:
But i'm really not sure this makes any sense?! Can anyone help me out of confusion? Is there another way of doing this or is this vaugely right?
Start with the solution in the form . There are two solutions for each value of n, namely
 and .
Looking at the second of these, the first thing you should notice is that 3–√10 is negative. In fact, (this follows from the fact that ). Therefore , and we can rewrite  as . This can be combined with  to form the single expression , which agrees with Plato's method for finding the solution.