Let Z be a complex number such that |Z|+Z=2+i | vedclass

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

Question

(D) Let $Z = a + ib$. Then $|Z| = \sqrt{a^2 + b^2}$. Given $|Z| + Z = 2 + i$. Substituting the values,we get $\sqrt{a^2 + b^2} + a + ib = 2 + i$. Comp

Vedclass · Accepted Answer

$\frac{5}{4}$

Vedclass · Answer

(D) Let $Z = a + ib$. Then $|Z| = \sqrt{a^2 + b^2}$. Given $|Z| + Z = 2 + i$. Substituting the values,we get $\sqrt{a^2 + b^2} + a + ib = 2 + i$. Comparing the real and imaginary parts,we get $b = 1$ and $\sqrt{a^2 + b^2} + a = 2$. Since $b = 1$,$\sqrt{a^2 + 1} = 2 - a$. Squaring both sides,$a^2 + 1 = (2 - a)^2$. $a^2 + 1 = 4 - 4a + a^2$. $4a = 3$,so $a = \frac{3}{4}$. Now,$|Z| = \sqrt{a^2 + b^2} = \sqrt{(\frac{3}{4})^2 + 1^2} = \sqrt{\frac{9}{16} + 1} = \sqrt{\frac{25}{16}} = \frac{5}{4}$.

Let $Z$ be a complex number such that $|Z|+Z=2+i$ (where $i=\sqrt{-1}$),then $|Z|$ is equal to

Similar Questions

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 relation among the following is:

Let $z$ be a complex number such that $|z| + z = 3 + i$ (where $i = \sqrt{-1}$). Then $|z|$ is equal to

If $\left|\frac{z-25}{z-1}\right|=5$,then $|z|=$

If $z$ is a complex number with $|z| \geq 5$,then the least value of $\left|z+\frac{2}{z}\right|$ is

The real part of $(1 - \cos \theta + 2i\sin \theta )^{-1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module