Let z be a complex number with non-zero imagi | vedclass

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

Question

Given that

$z 
eq \overline{ z }$

Let $\alpha=\frac{2+3 z+4 z^2}{2-3 z+4 z^2}=\frac{\left(2-3 z+4 z^2ight)+6 z}{2-3 z+4 z^2}$

$	herefore

Vedclass · Accepted Answer

$0.50$

Vedclass · Answer

Given that

$z 
eq \overline{ z }$

Let $\alpha=\frac{2+3 z+4 z^2}{2-3 z+4 z^2}=\frac{\left(2-3 z+4 z^2ight)+6 z}{2-3 z+4 z^2}$

$	herefore \alpha=1+\frac{6 z}{2-3 z+4 z^2}$

If $\alpha$ is a real number, then

$\alpha=\bar{\alpha}$

$\Rightarrow \frac{z}{2-3 z+4 z^2}=\frac{\bar{z}}{2-3 \bar{z}+4 \bar{z}^2}$

$	herefore 2(z-\bar{z})=4 z \bar{z}(z-\bar{z})$

$\Rightarrow(z-\bar{z})(2-4 z \bar{z})=0$

As $z 
eq \bar{Z}$ (Given)

$\Rightarrow z \bar{z}=\frac{2}{4}=\frac{1}{2}$

$\Rightarrow|z|^2=0.50$

Let $z$ be a complex number with non-zero imaginary part. If $\frac{2+3 z+4 z^2}{2-3 z+4 z^2}$ is a real number, then the value of $|z|^2$ is. . . . .

Similar Questions

The amplitude of $0$ is

The amplitude of $\frac{{1 + \sqrt 3 i}}{{\sqrt 3 + 1}}$ is

If $z = 3 + 5i,\,\,{\rm{then }}\,{z^3} + \bar z + 198 = $

If ${z_1}.{z_2}........{z_n} = z,$ then $arg\,{z_1} + arg\,{z_2} + ....$+$arg\,{z_n}$ and $arg$$z$ differ by a

The solution of the equation $|z| - z = 1 + 2i$ is