If m_1, m_2, m_3 and m_4 respectively denote | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $z_1 = 1+4i, z_2 = 3+i, z_3 = 1-i$ and $z_4 = 2-3i$.The modulus of a complex number $z = a+bi$ is given by $|z| = \sqrt{a^2+b^2}$.Calculating

Vedclass · Accepted Answer

$m_3 < m_2 < m_4 < m_1$

Vedclass · Answer

(C) Let $z_1 = 1+4i, z_2 = 3+i, z_3 = 1-i$ and $z_4 = 2-3i$.The modulus of a complex number $z = a+bi$ is given by $|z| = \sqrt{a^2+b^2}$.Calculating the moduli:$m_1 = |1+4i| = \sqrt{1^2+4^2} = \sqrt{1+16} = \sqrt{17}$$m_2 = |3+i| = \sqrt{3^2+1^2} = \sqrt{9+1} = \sqrt{10}$$m_3 = |1-i| = \sqrt{1^2+(-1)^2} = \sqrt{1+1} = \sqrt{2}$$m_4 = |2-3i| = \sqrt{2^2+(-3)^2} = \sqrt{4+9} = \sqrt{13}$Comparing the values: $\sqrt{2} < \sqrt{10} < \sqrt{13} < \sqrt{17}$,which implies $m_3 < m_2 < m_4 < m_1$.

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

Similar Questions

For the complex number $z$,which of the following is true for $z + \bar z$ and $z\,\bar z$?

Let $z_{1} = 2 - i$ and $z_{2} = -2 + i$. Find $\operatorname{Re}\left(\frac{z_{1} z_{2}}{\bar{z}_{1}}\right)$.

Let $z = a - \frac{i}{2}$,where $a \in R$. Then $|i + z|^2 - |i - z|^2$ is equal to

If $|z_1| = |z_2| = \dots = |z_n| = 1$,then the value of $|z_1 + z_2 + z_3 + \dots + z_n|$ is equal to:

The complex conjugate of $(4-3i)(2+3i)(1+4i)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module