Find the equation in cartesian coordinates of the locus of z if |z –

1.	Find the equation in cartesian coordinates of the locus of z if \|z – 5 + 6i\| = 5
Answer» Let z = x + iy \|z – 5 + 6i\| = 5 \|x + iy – 5 + 6i\| = 5 \|(x – 5) + i(y + 6)\| = 5 \(\sqrt{(x-5)^2+(y+6)^2}=5\) \(\therefore\) (x - 5)² + (y + 6)² = 25

Find the equation in cartesian coordinates of the locus of z if |z – 5 + 6i| = 5

Answer»

Let z = x + iy

|z – 5 + 6i| = 5

|x + iy – 5 + 6i| = 5

|(x – 5) + i(y + 6)| = 5

\(\sqrt{(x-5)^2+(y+6)^2}=5\)

\(\therefore\) (x - 5)² + (y + 6)² = 25