If z and w are two complex numbers such that | vedclass

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

Question

$|z| \cdot|w|=1 \quad z =$ $r e^{\left(	heta+\frac{\pi}{2}ight)} 	ext { and } w$ $=\frac{1}{r} e^{i 	heta}$

$\bar{z} \cdot w$ $=e^{-i\left(	h

Vedclass · Accepted Answer

$\bar zw\,\, =  - \,i$

Vedclass · Answer

$|z| \cdot|w|=1 \quad z =$ $r e^{\left(	heta+\frac{\pi}{2}ight)} 	ext { and } w$ $=\frac{1}{r} e^{i 	heta}$

$\bar{z} \cdot w$ $=e^{-i\left(	heta+\frac{\pi}{2}ight)} \cdot e^{i 	heta} $ $=e^{-i\left(\frac{\pi}{2}ight)}=-i$

$\mathrm{z} \cdot \overline{\mathrm{w}}$ $=\mathrm{e}^{i\left(	heta+\frac{\pi}{2}ight)} \cdot \mathrm{e}^{-\mathrm{i} 	heta}$ $=\mathrm{e}^{\mathrm{i}\left(\frac{\pi}{2}ight)}=\mathrm{i}$

If $z$ and $w$ are two complex numbers such that $|zw| = 1$ and $arg(z) -arg(w) =\frac {\pi }{2},$ then

Similar Questions

Modulus of $\left( {\frac{{3 + 2i}}{{3 - 2i}}} \right)$ is

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

If $z =2+3 i$, then $z ^{5}+(\overline{ z })^{5}$ is equal to.

Let $z_1, z_2 \in C$ such that $| z_1 + z_2 |= \sqrt 3$ and $|z_1| = |z_2| = 1,$ then the value of $|z_1 - z_2|$ is

The real value of $\theta$ for which the expression $\frac{{1 + i\,\cos \theta }}{{1 - 2i\cos \theta }}$ is a real number is $\left( {n \in I} \right)$