Let z be a complex number such that |z|+z=3+i | vedclass

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

Question

(D) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z| + z = 3 + i$.Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$.Equating

Vedclass · Accepted Answer

$\frac{5}{3}$

Vedclass · Answer

(D) Let $z = x + iy$,where $x, y \in \mathbb{R}$.Given $|z| + z = 3 + i$.Substituting $z = x + iy$,we get $\sqrt{x^2 + y^2} + x + iy = 3 + i$.Equating the real and imaginary parts:$y = 1$ and $\sqrt{x^2 + y^2} + x = 3$.Substituting $y = 1$ into the second equation:$\sqrt{x^2 + 1} = 3 - x$.Squaring both sides:$x^2 + 1 = (3 - x)^2 = 9 - 6x + x^2$.$1 = 9 - 6x$ $\Rightarrow 6x = 8$ $\Rightarrow x = \frac{4}{3}$.Now,$|z| = \sqrt{x^2 + y^2} = \sqrt{(\frac{4}{3})^2 + 1^2} = \sqrt{\frac{16}{9} + 1} = \sqrt{\frac{25}{9}} = \frac{5}{3}$.

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

Similar Questions

For real numbers $a$ and $b$,if $4a + i(3a - b) = b - 6i$ and $z = a + \frac{b}{4}i$,then $\frac{|z|}{a} = $

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

The number of non-zero integral solutions of the equation $|1 - i|^x = 2^x$ is

If $z = \cos \frac{\pi}{6} + i\sin \frac{\pi}{6}$,then:

If $\alpha$ is the modulus of $z_1=4+3 i$,then a point that does not lie in the region represented by $|z-\overline{z_1}| \leq \alpha$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module