Complex Numbers And Quadratic Equations question 648
Question: If $ m_1,m_2,m_3 $ and $ m_4 $ respectively denote the moduli of the complex numbers $ 1+4i,3+i,1-i $ and $ 2-3i, $ then the correct one, among the following is
Options:
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 $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ z_1=1+4i,z_2=3+i,z_3=1-iandz_4=2-3i $
$ \therefore m_1=| z_1 |,m_2=| z_2 |,m_3=| z_3 |andm_4=| z_4 | $
$ \Rightarrow {m_1}=\sqrt{17},m_2=\sqrt{10},m_3=\sqrt{2},andm_4=\sqrt{13}, $
$ \Rightarrow {m_3}<m_2<m_4<m_1. $
BETA
