Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$

Find the real numbers $x$ and $y$ if $(x-i y)(3+5 i)$ is the conjugate of $-6-24 i$

If $\frac{{z - \alpha }}{{z + \alpha }}\left( {\alpha  \in R} \right)$ is a purely imaginary number and $\left| z \right| = 2$, then a value of $\alpha $ is

If $z_{1}=2-i, z_{2}=1+i,$ find $\left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+1}\right|$

Find the modulus and argument of the complex numbers:

$\frac{1+i}{1-i}$

The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is