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

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

Complex Numbers and Quadratic Equations

Solution:

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