Question

If the complex number $z$ is purely imaginary then locus of $z$ is

• A. a straight line
• B. a circle with centre $(-\frac{1}{4},\frac{1}{2})$ and radius $\frac{\sqrt{5}}{4}$
• C. a circle with centre $(\frac{1}{4},-\frac{1}{2})$ and passing through origin
• D. neither a circle nor a straight line.

Answer 1

The correct option is A a straight line

Let the complex number be of the form $z=x+iy$.

Now if the complex number $z$ is a purely imaginary number then we've, $x=0$.

And $x=0$ is the equation of the imaginary axis.

So the locus of the complex number $z$ is a straight line.