Question

If $|z|=5$, then the points representing the complex number $-i+\frac{15}{z}$ lies on the circle

• A. whose centre is $(0,1)$ and radius $=3$
• B. whose centre is $(0,-1)$ and radius $=3$
• C. whose centre is $(1,0)$ and radius $=15$
• D. whose centre is $(-1,0)$ and radius $=15$

Answer 1

Answer: (B)

Let $w=-i+\frac{15}{z}$, then $i+w=\frac{15}{z}$
$\therefore |i+w|=\frac{15}{|z|}=3$
$\therefore$ Locus of $w$ is a circle with centre at $(0,-1)$ and radius $=3$