If ${e^{i\theta }} = \cos \theta + i\sin \theta $,then in $\Delta ABC$,the value of ${e^{iA}} \cdot {e^{iB}} \cdot {e^{iC}}$ is

The complex numbers $\sin x + i \cos 2x$ and $\cos x - i \sin 2x$ (where $i = \sqrt{-1}$) are conjugate to each other for:

The value of $\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}$ is

Solve: $i x^2 - 3 x - 2 i = 0$

If $z=x+iy$ is a complex number such that $\bar{z}^{\frac{1}{3}}=a+ib$,then the value of $\frac{1}{a^2+b^2}\left(\frac{x}{a}+\frac{y}{b}\right)$ is equal to

Evaluate: $\left| \frac{1}{2}(z_1 + z_2) + \sqrt{z_1 z_2} \right| + \left| \frac{1}{2}(z_1 + z_2) - \sqrt{z_1 z_2} \right|$