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

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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

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