$$i z^3+z^2-z+i=0 \Rightarrow|z|=$$

If $$\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$$, then the true statement among the following is

The number of integer solutions of the equation $$|1-i|^x=2^x$$ is

Let $$Z_1, Z_2$$ and $$Z_3$$ be three non zero complex numbers such that $$a=\left|Z_1\right|, b=\left|Z_2\right|$$ and $$c=\left|Z_3\right|$$, if the determinant $$\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0$$, then