Q. If $\alpha_{1},\alpha_{2},\ \alpha_{3}$ respectively denote the moduli of the complex numbers $- i,\frac{1}{3}(1 + i)$ and $- 1 + i$, then their increasing order is
A) $\alpha_{1},\alpha_{2},\alpha_{3}$
B) $\alpha_{3},\alpha_{2},\alpha_{1}$
C) $\alpha_{2},\alpha_{1},\alpha_{3}$
D) $\alpha_{3},\alpha_{1}{,\alpha}_{2}$
Explanation
(c)
Given, $\alpha_{1} = | - i| = 1$
$\alpha_{2} = \left| \frac{1}{3}(1 + i) \right| = \frac{1}{3}\sqrt{2}$
and $\alpha_{3} = | - 1 + i| = \sqrt{2}$
$\therefore$ The increasing order is $\alpha_{2},\ \alpha_{1},\ \alpha_{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.