The problem involves finding all solutions for the equation z^2 = 1 + 2i, where z is expressed in the form a + bi, with a and b being real numbers. The original poster expresses uncertainty about how to begin tackling the problem.
The discussion is ongoing, with participants exploring different approaches to the problem. There is no explicit consensus on a single method, but several lines of reasoning are being examined, including direct substitution and reformulation of the complex number.
The original poster specifies that numerical evaluation is not required for this problem, which may influence the methods discussed.
It seems that even if you don't have a good idea how to arrive at an answer, you have an obvious starting path: plug the answer form "z=a+bi" into the equation you're trying to solve. It may, or it may not, lead to something that works, but at least it's something to try.static said:Determine all solutions of z^2 = 1+2i in the form z=a+bi, where a and b are real numbers.
For this question numerical evaluation is not required. I just don't know how to start.