Question

If $|z-1-i|=1$, then the locus of a point represented by the complex number $5(z-i)-6$ is

• A. circle with centre (1, 0) and radius 3
• B. circle with centre (-1, 0) and radius 5
• C. line passing through origin
• D. line passing through (-1, 0)

Answer 1

The correct option is B

circle with centre (-1, 0) and radius 5

Let $w=5(z-i)-6$

$\Rightarrow |\omega +1|=5|z-1-i|=5$