If $\alpha_1, \alpha_2, \alpha_3$ respectively denote the moduli of the complex number $-i,…
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
$\alpha_1, \alpha_2, \alpha$
$\alpha_3, \alpha_2, \alpha_1$
$\alpha_2, \alpha_1, \alpha_3$
$\alpha_3, \alpha_1, \alpha_2$
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 $\alpha_2, \alpha_1, \alpha_3$.