find angle x such that 3+2isinx/1-2isinx is purely imaginary.pls don't give links Share with your friends Share 2 Mayank Jha answered this Dear student, 3 + 2i sin x1 - 2i sinxRationalizing this function. We get:3 + 2i sin x1 - 2i sinx *1 + 2i sinx1 + 2i sinx= (3 + 2i sin x)*(1 + 2i sinx)12 - (2i sin x)2=(3 + 2i sin x) +2i sin x*(3 + 2i sin x) 1 - 4i2 sin2x=3 + 2i sin x + 6i sin x + 4i2 sin2x1 + 4 sin2x=3 + 8i sin x - 4 sin2x1 + 4 sin2x=3 - 4 sin2x1 + 4 sin2x + 8i sin x1 + 4 sin2xSince the value should be purely imaginary. So, we can say:3 - 4 sin2x1 + 4 sin2x = 0⇒3 - 4 sin2x = 0⇒3 = 4 sin2x⇒sin2x = 34⇒sin x = ±32∴x= ±π3 Regards 4 View Full Answer