The points P and Q denote the complex numbers | vedclass

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(B) Given the condition $Z_1 \bar{Z}_2 + \bar{Z}_1 Z_2 = 0$. Dividing by $Z_2 \bar{Z}_2$ (assuming $Z_2 
eq 0$),we get $\frac{Z_1}{Z_2} + \frac{\bar{

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$1$

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(B) Given the condition $Z_1 \bar{Z}_2 + \bar{Z}_1 Z_2 = 0$. Dividing by $Z_2 \bar{Z}_2$ (assuming $Z_2 
eq 0$),we get $\frac{Z_1}{Z_2} + \frac{\bar{Z}_1}{\bar{Z}_2} = 0$. This implies $2 	ext{Re}(\frac{Z_1}{Z_2}) = 0$,which means $\frac{Z_1}{Z_2}$ is purely imaginary. Let $\frac{Z_1}{Z_2} = ki$ for some real $k 
eq 0$. Then $Z_1 = Z_2(ki) = |Z_1| e^{i 	heta_1}$ and $Z_2 = |Z_2| e^{i 	heta_2}$. The ratio $\frac{Z_1}{Z_2} = \frac{|Z_1|}{|Z_2|} e^{i(	heta_1 - 	heta_2)} = \frac{|Z_1|}{|Z_2|} e^{i 	heta}$. Since $\frac{Z_1}{Z_2}$ is purely imaginary,its argument must be $\pm \frac{\pi}{2}$. Therefore,$	heta = \pm \frac{\pi}{2}$. Thus,$\sin 	heta = \sin(\pm \frac{\pi}{2}) = \pm 1$. Given the options,the magnitude of $\sin 	heta$ is $1$.

The points $P$ and $Q$ denote the complex numbers $Z_1$ and $Z_2$ in the Argand plane. $O$ is the origin. If $Z_1 \bar{Z}_2 + \bar{Z}_1 Z_2 = 0$ and $\angle POQ = \theta$,then $\sin \theta = $

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