Question

If $\alpha ,\beta ,\gamma$ are modulus of the complex number $3+4i,-5+12i,1-i$, then the increasing order for $\alpha ,\beta$ and $\gamma$ is

• A. $\alpha ,\gamma ,\beta$
• B. $\alpha ,\beta ,\gamma$
• C. $\gamma ,\alpha ,\beta$
• D. can't be determined

Answer 1

Answer: (C)

$\gamma ,\alpha ,\beta$

$\alpha =\sqrt{3^2+4^2}=5$
$\beta =\sqrt{(5{)}^2+(12{)}^2}=13$
$\gamma =\sqrt{1+1^2}=\sqrt{2}$
$\Rightarrow \gamma <\alpha <\beta$