Question

If $|z|=1$, then the point representing the complex number $-1+3z$ will lie on

• A. A circle
• B. A straight line
• C. A parabola
• D. A hyperbola

Answer 1

Answer: (A)

A circle

Let
$\alpha =-1+3z$
$\alpha +1=3z$
Taking, modulus, we get
$|\alpha +1|=3|z|$
$|\alpha +1|=3\left(1\right)$
$|\alpha +1|=3$
Hence $\alpha$ lies on a circle.