Question

If $\left|z\right|=1$, 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

The correct option is A a circle

Let
$\alpha =-1+3z$
$\alpha +1=3z$
$|\alpha +1|=|3z|$
$|\alpha +1|=3|z|$
$|\alpha +1|=3$
This represents a circle with radius $3$ and center at $(-1,0)$.