If $Z=\frac{-2}{1+\sqrt{3} i}, i=\sqrt{-1}$, then the value of $\arg Z$ is

If $\left|\frac{\mathrm{z}}{1+\mathrm{i}}\right|=2$, where $\mathrm{z}=x+\mathrm{i} y, \mathrm{i}=\sqrt{-1}$ represents a circle, then centre ' $C$ ' and radius ' $r$ ' of the circle are

Let $\left(-2-\frac{1}{3} \mathrm{i}\right)^3=\frac{x+\mathrm{i} y}{27}, \mathrm{i}=\sqrt{-1}$, where $x$ and $y$ are real numbers, then $(y-x)$ has the value

If $z^2+z+1=0$ then $\left(z^3+\frac{1}{z^3}\right)^2+\left(z^4+\frac{1}{z^4}\right)^2=$ where $z=w=$ complex cube root of unity