Question

If $|z+2+3i|=5$, then the locus of $z$ is:

• A. A circle with centre $(2,3)$ and radius $25$ units
• B. A circle with centre $(-2,-3)$ and radius $25$ units
• C. A circle with centre $(2,3)$ and radius $5$ units
• D. A circle with centre $(-2,-3)$ and radius $5$ units

Answer 1

The correct option is D A circle with centre $(-2,-3)$ and radius $5$ units

we know
$|z-z_1|=c$
represents a circle with center at $z_1$ and radius = $c$ in complex plane
Comparing with $|z+2+3i|=5$
or $|z-(-2-3i\left)\right|=5$
Hence, the locus is a circle with centre at $(-2,-3)$ and radius $5$