If z is a complex number such that frac{{z - | vedclass

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

Question

(b) Let $\frac{{z - 1}}{{z + 1}} = iy$ where $y \in R$
This gives $z = \frac{{1 + iy}}{{1 - iy}} = \frac{{1 + iy}}{{1 - iy}} 	imes \frac{{1 + iy}}{{

Vedclass · Accepted Answer

$|z|\, = 1$

Vedclass · Answer

(b) Let $\frac{{z - 1}}{{z + 1}} = iy$ where $y \in R$
This gives $z = \frac{{1 + iy}}{{1 - iy}} = \frac{{1 + iy}}{{1 - iy}} 	imes \frac{{1 + iy}}{{1 + iy}} = \frac{{(1 - {y^2}) + 2iy}}{{1 + {y^2}}}$
$	herefore $ $|z| = \frac{1}{{1 + {y^2}}}\sqrt {{{(1 - {y^2})}^2} + 4{y^2}} = \frac{{1 + {y^2}}}{{1 + {y^2}}} = 1$.

If $z$ is a complex number such that $\frac{{z - 1}}{{z + 1}}$ is purely imaginary, then

Similar Questions

If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is

The maximum value of $|z|$ where z satisfies the condition $\left| {z + \frac{2}{z}} \right| = 2$ is

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

If $arg\, z < 0$ then $arg\, (-z)\, -arg(z)$ is equal to

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