The number of solutions of the system of equations $2 x+y-z=7, x-3 y+2 z=1, x+4 y-3 z=5$ is

The points in the argand plane represented by the complex numbers $4 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 6 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ form

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

If $x^6=(\sqrt{3}-i)^5$, then the product of all of its roots is