Question

If $m_1$, $m_2$, $m_3$ and $m_4$ respectively denote the moduli of the complex numbers $1+4i,3+i,1–iand2–3i$ then the correct order among the following is :

• A. $m_1$<$m_2$<$m_3$<$m_4$
• B. $m_4$<$m_3$<$m_2$<$m_1$
• C. $m_3$<$m_2$<$m_4$<$m_1$
• D. $m_3$<$m_1$<$m_2$<$m_4$

Answer 1

The correct option is C $m_3$<$m_2$<$m_4$<$m_1$

$m_1=|1+4i|=\sqrt{1+16}=\sqrt{17}$.
$m_2=|3+i|=\sqrt{9+1}=\sqrt{10}$
$m_3=|1-i|=\sqrt{1+1}=\sqrt{2}$
$m_4=|2-3i|=\sqrt{4+9}=\sqrt{13}$
Hence
$m_1>m_4>m_2>m_3$