Question

If the complex number $z$ lies on a circle with centre at the origin and radius $\frac{1}{4}$, then the complex number $-1+8z$ lies on a circle with radius

• A. $4$
• B. $1$
• C. $3$
• D. $2$

Answer 1

Answer: (D)

$2$

Given: $|z|=\frac{1}{4}$
Let $z^{\prime }=-1+8z$
$⟹z=\frac{z^{\prime }+1}{8}\Rightarrow |z|=\frac{|z^{\prime }+1|}{8}$
$⟹\frac{1}{4}=\frac{|z^{\prime }+1|}{8}\Rightarrow |z^{\prime }+1|=2$
$\therefore z^{\prime }$ lies on a circle with centre $(-1,0)$ and radius $2$.