The expression frac{3+2 i sin theta}{1-2 i si | vedclass

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(C) Let $z = \frac{3+2 i \sin 	heta}{1-2 i \sin 	heta}$.To make $z$ purely imaginary,its real part must be zero.Multiply the numerator and denominat

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$n \pi \pm \frac{\pi}{3}$

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(C) Let $z = \frac{3+2 i \sin 	heta}{1-2 i \sin 	heta}$.To make $z$ purely imaginary,its real part must be zero.Multiply the numerator and denominator by the conjugate of the denominator $(1+2 i \sin 	heta)$:$z = \frac{(3+2 i \sin 	heta)(1+2 i \sin 	heta)}{(1-2 i \sin 	heta)(1+2 i \sin 	heta)}$$z = \frac{3 + 6 i \sin 	heta + 2 i \sin 	heta + 4 i^2 \sin^2 	heta}{1 + 4 \sin^2 	heta}$Since $i^2 = -1$,we have:$z = \frac{(3 - 4 \sin^2 	heta) + i(8 \sin 	heta)}{1 + 4 \sin^2 	heta}$For $z$ to be purely imaginary,$	ext{Re}(z) = 0$:$\frac{3 - 4 \sin^2 	heta}{1 + 4 \sin^2 	heta} = 0$$3 - 4 \sin^2 	heta = 0$$\sin^2 	heta = \frac{3}{4}$$\sin 	heta = \pm \frac{\sqrt{3}}{2}$This implies $	heta = n \pi \pm \frac{\pi}{3}$.

The expression $\frac{3+2 i \sin \theta}{1-2 i \sin \theta}$ will be purely imaginary,if $\theta$ is equal to

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