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 \(z\).