Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2013 / Analysis / 4 / c / Solution

Write $z=x+iy$. Both moduli are nonnegative, so squaring preserves their strict inequality:ThusThe boundary is the perpendicular bisector of $0$ and $i$ in the complex plane; the strict inequality selects the half-plane containing $0$.