Complex Numbers...

For the equations $$x^2 + bx + c = 0$$ and $$2x^2 + (b + 1)x + c + 1 = 0$$ select the correct alternative

Consider the equation $$x^3 - nx + 1 =0$$, $$n\ \epsilon \  N$$ , $$n \geq  3$$. Then

The equation $$x^2 + nx + m = 0,$$ where $$n, m \in  I$$ can not have:

If $$x=1+i$$ is a root of the equation $$x^3-ix+1-i=0$$, then the other real root is

If the argument of a complex number is $$\cfrac { \pi  }{ 2 } $$, then the number is:

Total number of integral values of $$a$$ so that $$x^2-(a+1)x+a-1=0$$ has integral roots is equal to

If $$\overline { z } $$ lies in the third quadrant then $$z$$ lies in the

If $$a,b,c,d$$ are four consecutive terms of an increasing A.P, then the roots of the equation 
$$(x-a)(x-c)+2(x-b)(x-d)=0$$ are

$$p + iq = (2 - 3i) (4 + 2i)$$ then $$q$$ is

If $${ x }^{ 2 }+{ y }^{ 2 }=1$$ then value of $$\dfrac { 1+x+iy }{ 1+x-iy } $$ is