Question

A value of θ for which $\frac{2+3isin\theta }{1-2isin\theta }$ is purely imaginary, is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\frac{2+3isin\theta }{1-2isin\theta }\times \frac{1+2isin\theta }{1+2isin\theta }$
$\Rightarrow 2-6si{n}^2\theta =0\Rightarrow si{n}^2\theta =\frac{1}{3}$
$\therefore sin\theta =\pm \frac{1}{\sqrt{3}}$