Question

If $|z|=2$, then the points representing the complex number $-1+5z$ will lie on a circle whose radius r are given by

• A. $10$
• B. $25$
• C. $12$
• D. none of these

Answer 1

The correct option is A $10$

Let $z=x+iy$.

Now, $|z|=2$ gives,

$x^2+y^2=2^2$.....(1).

Again let, $-1+5z=h+ik$

or, $z=\frac{h+1}{5}+\frac{k}{5}$

or, $x=\frac{h+1}{5},y=\frac{k}{5}$.

Using these values in (1) we get,

$(h+1{)}^2+k^2=(10{)}^2$.

This represents a circle whose center is $(-1,0)$.

So the radius of the circle is $10$.