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)

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