# Locus of Complex Numbers

Locus of Complex Numbers is obtained by letting $z = x+yi$ and simplifying the expressions. Operations of modulus, conjugate pairs and arguments are to be used for determining the locus of complex numbers.

### Worked Example of Locus of Complex Numbers

Let $z = x + iy$ be a complex number such that $|z-1|^2 – |z-3|^2 = 1$. Find the locus of all complex numbers $z$.