Q47 / 120 · VITEEE 2015 · Mathematics

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

  • A
    4
  • B
    1
  • C
    3
  • Correct answer
    D
    2

Solution

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

Hence, the correct answer is option: 'D'.

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