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 \(z\).