Question

If $|z|=2$, then the locus of $1+5z$ is a circle whose centre is :

• A. ($-$$1,0)$
• B. $(1,0)$
• C. $(0,-1)$
• D. $(0,0)$

Answer 1

The correct option is B $(1,0)$

Let $t=1+5z$
$\Rightarrow t-1=5z$
$\Rightarrow |t-1|=5\left|z\right|=10[given\left|z\right|=2]$
comparing with $|z-z_0|=r$,
The locus of $t$ is a circle with radius $=10$ units and centre at $(1,0)$