Question

$|z-i|=5$ can be drawn as:

• A. circle of radius $1$ with centre $5i$
• B. circle of radius $5$ with centre $i$
• C. circle of radius $5$ with centre $-i$
• D. none of these

Answer 1

The correct option is B circle of radius $5$ with centre $i$

$|z-i|=5$

let $z=x+iy$

$\Rightarrow |x+iy-i|=5$

$\Rightarrow {|x+i(y-1)|}^2=5^2$

$\Rightarrow x^2+{(y-1)}^2=5^2$

radius = $5$

centre $(0,i)$