Q61 / 160 · AP EAMCET 2005 · Mathematics

If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex number $-i, \frac{1}{3}(1+i)$ and $-1+i$, then their increasing order is

  • A
    $\alpha_1, \alpha_2, \alpha$
  • B
    $\alpha_3, \alpha_2, \alpha_1$
  • Correct answer
    C
    $\alpha_2, \alpha_1, \alpha_3$
  • D
    $\alpha_3, \alpha_1, \alpha_2$

Solution

Given that $\begin{aligned} & \alpha_1=|-i|=1 \\ & \alpha_2=\left|\frac{1}{3}(1+i)\right|=\frac{1}{3} \sqrt{2} \\ & \alpha_3=|-1+i|=\sqrt{2} \end{aligned}$ $\therefore$ The increasing order is $\alpha_2, \alpha_1, \alpha_3$.

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

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