Question

$|z-i|=\sqrt{2}$ is a circle then find the centre and radius of the circle.

Answer 1

Given the equation of the circle is $|z-i|=\sqrt{2}$.

This equation can be written as,

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

Now squaring both sides we get,

$x^2+(y-1{)}^2=2$.

It is clear that the centre is at $(0,1)$ and radius is $\sqrt{2}$.