If the amplitude of $(z-2)$ is $\frac{\pi}{2}$, then the locus of $z$ is

If $\omega$ is the cube root of unity, $$ \frac{a+b \omega+c \omega^2}{c+a \omega+b \omega^2}+\frac{a+b \omega+c \omega^2}{b+c \omega+b \omega^2}= $$

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 $\frac{\pi}{4}$,