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