Discussion Forum

If  the complex number z lies on a circle  with centre at the origin and radius 1/4, then the complex number -1+8z lies  on a circle with radius

Answer:

Explanation:

Given : |z|=$\frac{1}{4}$

Let z'=-1+8z

$\Rightarrow  z=\frac{z'+1}{8}\Rightarrow|z|=\frac{|z'+1|}{8}$

 $\Rightarrow  \frac{1}{4}=\frac{|z'+1|}{8}\Rightarrow |z'+1|=2$

 $\therefore$    z' lies ona circle with centre (-1,0) and radius 2.