Argand Plane and Polar Representation

Find the modulus and the argument of the complex number $z=-\sqrt{3}+i$.

Find the modulus and the argument of the complex number $z=-1-i\sqrt{3}$.

The polar form of $\frac{1+3i}{1-2i}$ is $\sqrt{p}\left(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4}\right)$, then the value of $p$.

The polar form of $\frac{1+7i}{(2-i{)}^2}$ is $\sqrt{p}\left(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4}\right)$, then the value of $p$.

The polar form of $i$ is $\cos \frac{\pi }{p}+i\sin \frac{\pi }{p}$, then the value of $p$.

The polar form of $\sqrt{3}+i$ is $k\left(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\right)$, then the value of $k$.

If the given complex number $–3$ in polar form is $k(\cos m\pi +i\sin n\pi )$, then $k+m=$

If the representation of the complex number $\left(-1-i\right)$ in polar form is $\sqrt{m}\left(\cos \frac{-3\pi }{n}+i\sin \frac{-3\pi }{n}\right)$, then find the value of $\left(m+n\right)$.

The polar form of $-1+i$ is $\sqrt{k}\left(\cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4}\right)$, then the value of $k$.

The polar form of $1-i$ is $\sqrt{k}\left[\cos \left(-\frac{\pi }{4}\right)+i\sin \left(-\frac{\pi }{4}\right)\right]$, then the value of $k$.