Find the equation in cartesian coordinates of the locus of z if |z - 3

1.	Find the equation in cartesian coordinates of the locus of z if \|z - 3\| = 2
Answer» Let z = x + iy \|z – 3\| = 2 \|x + iy – 3\| = 2 \|(x – 3) + iy\| = 2 \(\sqrt{(x-3)^2+y^2}=2\) \(\therefore\) (x - 3)² + y² = 4

Find the equation in cartesian coordinates of the locus of z if |z - 3| = 2

Answer»

Let z = x + iy

|z – 3| = 2

|x + iy – 3| = 2

|(x – 3) + iy| = 2

\(\sqrt{(x-3)^2+y^2}=2\)

\(\therefore\) (x - 3)² + y² = 4