If $i z^3+z^2-z+i=0$ (where $z$ is a complex number),then the value of $|z|$ is

If $z_1$ and $z_2$ are two unimodular complex numbers that satisfy $z_1^2 + z_2^2 = 5,$ then $(z_1 - \bar{z}_1)^2 + (z_2 - \bar{z}_2)^2$ is equal to -

If $Z_1, Z_2, Z_3$ are three complex numbers with unit modulus such that $|Z_1-Z_2|^2+|Z_1-Z_3|^2=4$,then $Z_1 \overline{Z_2}+\overline{Z_1} Z_2+Z_1 \overline{Z_3}+\overline{Z_1} Z_3=$

The value of $\sum_{n=0}^{\infty}\left(\frac{2 i}{3}\right)^n$ is

If $x = 1 + 2i$,then the value of $x^3 + 7x^2 - x + 16$ is

If a complex number $z$ is such that $(7+i)(z+\bar{z})-(4+i)(z-\bar{z})+116i=0$,then $z\bar{z}=$