Question

If $|z|=2$, then the points representing the complex numbers $-1+5z$ will lie on a

• A. Circle
• B. Straight line
• C. Parabola
• D. None of these

Answer 1

The correct option is A Circle

$\left|z\right|=2$

Let $z^{\prime }=x+iy$ lies on the locus represented by the complex numbers $-1+5z$

So,

$z^{\prime }=-1+5z$

$z^{\prime }+1=5z$

$|z^{\prime }+1|=\left|5z\right|$

$|z^{\prime }+1|=5\left|z\right|=5\left(2\right)=10$

$|x+iy+1|=10$

$\Rightarrow (x+1{)}^2+y^2=100$

which is an equation of a circle with radius $10$ and center $(-1,0)$