Question

If $arg(z-2-3i)=\frac{\pi }{2}$ then the locus of $z$ is:

• A. Straight line
• B. An ellipse
• C. A circle
• D. A parabola

Answer 1

The correct option is A Straight line

Let
$z=x+iy$
Hence substituting in the above equation, we get
$z=(x-2)+i(y-3)$
The real part of $z$ is zero.
Hence,
$x-2=0$
$x=2$
Hence, the locus of $z$ is a straight line.