If the real part of is 4, then show that the locus of the point representing z in the complex plane is a circle.

Let z = x + iy

Now,

Given that real part is 4.

⇒ x² + x – 2 + y² = 4 (x² – 2x + 1 + y²)

⇒ 3x² + 3y² – 9x + 6 = 0

Which represents a circle.

Hence, locus of z is a circle.