Question

If $|z|=1$ and $w=-1+3z$, then the locus of $w$ on argand plane is

• A. a circle whose centre is at $(-1,0)$ and radius is $3$ units.
• B. a circle whose centre is at $(-1,0)$ and radius is $9$ units.
• C. a circle whose centre is at $(0,-1)$ and radius is $3$ units.
• D. a circle whose centre is at $(1,0)$ and radius is $3$ units.

Answer 1

The correct option is A a circle whose centre is at $(-1,0)$ and radius is $3$ units.

Given : $|z|=1,w=-1+3z$
Now,
$w+1=3z\Rightarrow |w+1|=3|z|\Rightarrow |w+1|=3$
Let $w=x+iy$, then
$(x+1{)}^2+y^2=9$
Which is a equation of circle whose center is at $(-1,0)$ and radius is $3\text{units}$