1. The problem statement, all variables and given/known data Let A be complex, B be real. Show [itex]\left|z^2\right|[/itex]+ Re(Az)+B=0 only has a solution if and only if [itex]\left|A^2\right|[/itex][itex]\geq4B[/itex]. Then, assuming the above condition holds, show the solution is a circle or a single point. 2. Relevant equations General quadratic equation I think? 3. The attempt at a solution Well, as above, I know the general quadratic equation for z, but I am not sure if the absolute value thing affects it and otherwise I am lost. My suspicion is that the solution will be a real number and since all of the coefficients are real, when using the quadratic equation, you need to have whats under the radical be positive. Something along those lines I think. I, however, have no clue how to prove it somewhat rigorously.