Complex Numbers...

If $$(1 - i\sqrt {3})^{2} (z) (4i) = (1 + i\sqrt {3})$$, then $$Amp\ z$$ is

If the equation $$x^2 - bx + 1 = 0$$ does not possess real roots, then

If $$ z = \dfrac {-1}{2} + i \dfrac {\sqrt3}{2} $$, then $$ 8 + 10z + 7z^2 $$ is equal to :

If the complex numbers $$z_1, z_2$$ and $$z_3$$ denote the vertices of an isosceles triangle, right angled at $$z_1$$, then $$(z_1 - z_2)^2 + (z_1 - z_3)^2$$ is equal to

If $$z$$ is a complex number such that $$z + |z| = 8 + 12i$$, then the value of $$|z^{2}|$$ is

Which of the given alternatives represent a point in Argand plane, equidistant from roots of the equation $$(z+1)^4= 16z^4$$?

The number of values k for which  $$[x^2- (k -2)x + k^2$$][$$x^2+kx+(2k-1)]$$  is a perfect square is

Let$$ z$$ = $$\cos\theta + i \sin\theta$$. Then the value of $$\sum\limits_{m=1}^15Im( z^{2m-1})$$ at $$\theta = 2^0$$ is 

If $$z_1, z_2$$ are two complex numbers such that $$arg(z_1+z_2)=0$$ and $$Im(z_1z_2)=0$$, then.

The principal value of $$arg(z)$$ lies in the interval: