Question

If $-1+\sqrt{-3}=r{e}^{\theta }$ , then θ is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Here $-1+\sqrt{-3}=r{e}^{\theta }\Rightarrow -1+i\sqrt{3}=r{e}^{\theta }$
$=rcos\theta +irsin\theta$
Equating real and imaginary parts,we get $rcos\theta =-1andrsin\theta =\sqrt{3}$

Hence, $tan\theta =-\sqrt{3}\Rightarrow tan\theta =tan\frac{2\pi }{3},$ Hence $\theta =\frac{2\pi }{3}.$