Let A =left{theta in(0,2 pi): frac{1+2 i sin | vedclass

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Question

$z=\frac{1+2 i \sin 	heta}{1-i \sin 	heta} 	imes \frac{1+i \sin 	heta}{1+i \sin 	heta}$

$z=\frac{1-2 \sin ^2 	heta+i(3 \sin 	heta)}{1+\sin ^

Vedclass · Accepted Answer

$4 \pi$

Vedclass · Answer

$z=\frac{1+2 i \sin 	heta}{1-i \sin 	heta} 	imes \frac{1+i \sin 	heta}{1+i \sin 	heta}$

$z=\frac{1-2 \sin ^2 	heta+i(3 \sin 	heta)}{1+\sin ^2 	heta}$

$\operatorname{Re}(z)=0$

$\frac{1-2 \sin ^2 	heta}{1+\sin ^2 	heta}=0$

$\sin 	heta=\frac{ \pm 1}{\sqrt{2}}$

$A=\left\{\frac{\pi}{4}, \frac{3 \pi}{4}, \frac{5 \pi}{4}, \frac{7 \pi}{4}ight\}$

$	ext { sum }=4 \pi(	ext { Option } 3)$

Let $A =\left\{\theta \in(0,2 \pi): \frac{1+2 i \sin \theta}{1- i \sin \theta}\right.$ is purely imaginary $\}$. Then the sum of the elements in $A$ is

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