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TS EAMCET · Maths · Complex Number

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

  1. A \(\alpha_1, \alpha_2, \alpha\)
  2. B \(\alpha_3, \alpha_2, \alpha_1\)
  3. C \(\alpha_2, \alpha_1, \alpha_3\)
  4. D \(\alpha_3, \alpha_1, \alpha_2\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\alpha_2, \alpha_1, \alpha_3\)

Step-by-step Solution

Detailed explanation

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 \(\alpha_2, \alpha_1, \alpha_3\).