Question

In a complex plane, the point $z$ moves such that $|z-3i|=2$ then its locus is

• A. a straight line
• B. a circle
• C. y-axis
• D. None of these

Answer 1

Answer: (B)

$|z-3i|=2$
$\Rightarrow$ $|x+iy-3i|=2$
$\Rightarrow$ $|x(y-3)i|=2$
$\Rightarrow$ $\sqrt{x^2+{(y-3)}^2}=2$
$\Rightarrow$ $x^2+{(y-3)}^2=4;$
which represents a circle.