If $x = 3 - 2\sqrt{3}i$,then $x^4 - 12x^3 + 54x^2 - 108x - 54 = $

If $z=x-iy$ and $z^{1/3}=a+ib$,then $\frac{(x/a+y/b)}{a^2+b^2}=$

The product of the real roots of the equation $4x^4 - 24x^3 + 57x^2 + 18x - 45 = 0$,given that one of the roots is $3 + i\sqrt{6}$,is:

The real part of $(1-\cos \theta+i \sin \theta)^{-1}$ is

If $\alpha+i \beta$ and $\gamma+i \delta$ are the roots of $x^2-(3-2 i) x-(2 i-2)=0$,where $i=\sqrt{-1}$,then $\alpha \gamma+\beta \delta$ is equal to :

The biquadratic equation,two of whose roots are $1+i$ and $1-\sqrt{2}$,is