Question

If $\left|z\right|=1,$ then point representing the complex number $-2+3z$ will lie on

• A. a straight line
• B. a circle
• C. the real axis
• D. on imaginary axis

Answer 1

Answer: (B)

a circle

Let $z^{\prime }=-2+3z$

$\Rightarrow z^{\prime }+2=3z$

$\Rightarrow |z^{\prime }+2|=3\left|z\right|$

$\Rightarrow |z^{\prime }+2|=3$

$z^{\prime }$ lies on a circle.