Question

When $|z|=1$, the point $1+2z$ lie on a

• A. circle with radius 1 and centre $(0,1)$
• B. circle with radius 2 and centre $(1,0)$
• C. straight line
• D. circle with radius 3 and centre at the origin

Answer 1

Answer: (B)

Let $w=1+2z$. Then $w-1=2z$
$\therefore |w-1|=2|z|=2$ for points on $|z|=1$
Hence, the locus of $w$ is a circle with centre at $(1,0)$ and radius $2$ when $|z|=1$.