Question

A point $z$ moves on Argand diagram in such a way that $|z-3i|=2$, then its locus will be

• A. $y$ axis
• B. Straight line
• C. Parabola
• D. None of these

Answer 1

The correct option is D

None of these

Explanation for correct option:

Finding the locus:

Given, $|z-3i|=2$

Put $z=x+iy$

$\Rightarrow$$|x+iy–3i|=2$

$\Rightarrow$$|x+(y-3\left)i\right|=2$

Take modulus and square both sides, we get

${\left[\sqrt{x^2+{\left(y-3\right)}^2}\right]}^2=2^2$

$\Rightarrow$ $x^2+{(y-3)}^2=4$

This equation represents a circle.

Hence, Option ‘D’ is Correct.