If $\frac{3-2 i \sin heta}{1+2 i \sin heta}$ is purely imaginary number, then $ heta=$

Question

If $\frac{3-2 i \sin 	heta}{1+2 i \sin 	heta}$ is purely imaginary number, then $	heta=$

Aicharya · Accepted Answer

$\frac{3-2 i \sin 	heta}{1+2 i \sin 	heta}=\frac{(3-2 i \sin 	heta)(1-2 i \sin 	heta)}{1+4 \sin ^2 	heta}=\frac{3-4 \sin ^2 	heta}{1+4 \sin ^2 	heta}$ From the given information real part $=0$ $\Rightarrow \sin ^2 	heta=\frac{3}{4} \Rightarrow 	heta=n \pi \pm \frac{\pi}{3}$

If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$

Solution