Question

If the imaginary part of the expression $\frac{e^{i\theta }}{z-2}+\frac{z-2}{e^{i\theta }}$ is zero, then the locus of $z$ is (where $\theta$ is a constant such that $\theta \ne \arg (z-2)$ )

• A. a straight line parallel to $x$-axis
• B. a parabola
• C. a circle of radius 1 and centre $(2,0)$
• D. a straight line parallel to $y$-axis

Answer 1

Answer: (C)

Correct answer is (c) a circle of radius 1 and centre $(2,0)$