MHTCET 11 Apr 2026 Shift 1 Paper

Concept:A complex number can be written in polar form as $re^{i\theta}$, where $\theta$ is the argument determined by the quadrant of the point.Explanation:Given,$$-1+\sqrt{-3}=re^{i\theta}$$Since $\sqrt{-3}=i\sqrt{3}$, we get:$$-1+\sqrt{-3}=-1+i\sqrt{3}$$The real part is $-1$ and the imaginary part is $\sqrt{3}$. So the point is $(-1,\sqrt{3})$, which lies in the second quadrant. Now,$$\tan\theta=\frac{\text{imaginary part}}{\text{real part}}=\frac{\sqrt{3}}{-1}=-\sqrt{3}$$The reference angle is $\frac{\pi}{3}$. Since the point is in the second quadrant:$$\theta=\pi-\frac{\pi}{3}=\frac{2\pi}{3}$$Thus, the value of $\theta$ is $\frac{2\pi}{3}$.Answer:$$\theta=\frac{2\pi}{3}$$Correct option: D.