If m1,m2,m3 and m4 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

Question

If m1,m2,m3 and m4 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 (A) m1 < m2 < m3< m4 (B) m4 < m3 < m2< m1 (C) m3 < m2 < m4< m1 (D) m3 < m1 < m2 < m4

Tardigrade Admin · Accepted Answer

Let z1= 1 + 4i, z2 = 3 + i, z3 = 1 - i and z4= 2-3i ∴ m1=|z1|, m2=|z2|, m3=|z3| and m4=|z4| ⇒ m1=√1+42, m2=√32+12 m3=√12+12 and m4=√22+32 ⇒ m1=√17, m2=√10 m3=√2 and m4=√13 ⇒ m3 < m2 < m4 < m1

Q. If $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively denote the moduli of the complex numbers $1 + 4 i, 3 + i, 1 - i$ and $2 - 3 i$ , then the correct one, among the following is

$m_{1} < m_{2} < m_{3} < m_{4}$

$m_{4} < m_{3} < m_{2} < m_{1}$

$m_{3} < m_{2} < m_{4} < m_{1}$

$m_{3} < m_{1} < m_{2} < m_{4}$

Q. If m1​,m2​,m3​ and m4​ 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

m1​<m2​<m3​<m4​

m4​<m3​<m2​<m1​

m3​<m2​<m4​<m1​

m3​<m1​<m2​<m4​

Let z1​=1+4i, z2​=3+i, z3​=1−i and z4​=2−3i ∴m1​=∣z1​∣,m2​=∣z2​∣,m3​=∣z3​∣ and m4​=∣z4​∣ ⇒m1​=1+42​,m2​=32+12​ m3​=12+12​ and m4​=22+32​ ⇒m1​=17​,m2​=10​ m3​=2​ and m4​=13​ ⇒m3​<m2​<m4​<m1​

Q. If $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively denote the moduli of the complex numbers $1 + 4 i, 3 + i, 1 - i$ and $2 - 3 i$ , then the correct one, among the following is

$m_{1} < m_{2} < m_{3} < m_{4}$

$m_{4} < m_{3} < m_{2} < m_{1}$

$m_{3} < m_{2} < m_{4} < m_{1}$

$m_{3} < m_{1} < m_{2} < m_{4}$