If $a$ is the root of equation $z^n+2 z^{n-1}+3 z^{n-2}+12-18 z=0$ which lies inside $|z|=1$, then

If $\alpha$ is a root of $x^4=1$ with negative principal argument, then the principle argument of $\Delta(A)$, where $\Delta(A)=\left|\begin{array}{ccc}1 & 1 & 1 \\ \alpha^n & \alpha^{n+1} & \alpha^{n+3} \\ \frac{1}{\alpha^{n+1}} & \frac{1}{\alpha^n} & 0\end{array}\right|$

The complex number $z$ satisfying $z+|z|$ $=1+7 i$, then the value of $|z|^2$ equals

If $$z_1, z_2$$ and $$z_3$$ are the vertices $$A, B$$ and $$C$$ respectively of an isosceles right angled triangle with right angled at $$C$$, then $$\left(z_1-z_3^{\prime}\right)\left(z_2-z_3\right)$$ equals to