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$\frac{5 + i \sin θ}{5 - 3 i \sin θ}$ is a real number when

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θ=π/4

θ=−π

θ=−π/2

θ=π/2

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Correct option is B

5+isin⁡θ5−3isin⁡θ is a real number⇔ 5+isin⁡θ5−3isin⁡θ=5−isin⁡θ5+3isin⁡θ⇔ (5+isin⁡θ)(5+3isin⁡θ)=(5−3isin⁡θ)(5−isin⁡θ)=25−20isin⁡θ−3sin2⁡θ⇔40isin⁡θ=0⇔sin⁡θ=0This is possible when θ=-π

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5+isin⁡θ5−3isin⁡θ is a real number when

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$\frac{5 + i \sin θ}{5 - 3 i \sin θ}$ is a real number when