Find sum of all possible value of θ in the interval (−2π,π) for which 1−2siniθ3+2isinθ is purely imaginary (a) 3π (b) (π) (c) 32π (d) 2π

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Find sum of all possible value of in the interval {(-{{}}{{2}

Question

Find sum of all possible value of $θ$ in the interval $(- \frac{π}{2}, π)$ for which $\frac{3 + 2 i sin θ}{1 - 2 sin i θ}$ is purely imaginary (a) $\frac{π}{3}$ (b) $(π)$ (c) $\frac{2 π}{3}$ (d) $\frac{π}{2}$

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Lucas Discussed

Find sum of all possible value of

θ

in the interval

(- \frac{π}{2}, π)

for which

\frac{3 + 2 i sin θ}{1 - 2 sin i θ}

is purely imaginary (a)

\frac{π}{3}

(b)

(π)

(c)

\frac{2 π}{3}

(d)

\frac{π}{2}

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Question Text

Find sum of all possible value of

θ

in the interval

(- \frac{π}{2}, π)

for which

\frac{3 + 2 i sin θ}{1 - 2 sin i θ}

is purely imaginary (a)

\frac{π}{3}

(b)

(π)

(c)

\frac{2 π}{3}

(d)

\frac{π}{2}