If $(3+i)$ is a root of $x^2+a x+b=0$, then $a=$

If $z_1=10+6 i, z_2=4+6 i$ and $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_2\right)}$ is $\frac{\pi}{4}$,

If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$

If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$