Complex Numbers...

If $$|Z|=2,|z_{2}|=3,|z_{3}=4|$$ and $$|z_{1}+z_{2}+z_{3}|=5$$ then $$|4z_{2}z_{3}+9z_{3}z_{1}+16z_{1}z_{2}|=$$

If $$\dfrac{x - 3}{3 + i} + \dfrac{y - 3}{3 - i} = i $$ where $$x , y \in R$$ then

Consider two quadratic expressions $$f(x)=ax^2+bx+c$$ and $$g(x)=ax^2+px+q$$, $$(b\neq q)$$ such that their discriminants are equal. If $$f(x)=g(x)$$ has a root $$x=\alpha$$, then?

The complex number $$\dfrac{1 + 2i}{1 - i}$$ lies in which quadrant of the complex plane.

Given $$\left| z \right| =4$$ and $$Argz=\dfrac{5z}{6}$$, then $$z$$ is

The locus of $$z$$ such that $$\left| {\dfrac{{z + i}}{{z - 1}}} \right| = 2$$

$$\left(\dfrac{1 + i}{1 - i}\right)^4 + \left(\dfrac{1 - i}{1 + i}\right)^4 = $$ 

In the graph of the parametric equations $$\begin{cases} x={ t }^{ 2 }+t \\ y={ t }^{ 2 }-t \end{cases}$$ for integral values of t.

If $$\left| {z - 1} \right| = 2$$, then the value of $$z\overline z  - z - \overline z $$ is equal to: 

If $$a < b < c < d$$, then the roots of the equation $$(x-a)(x-c)+2(x-b)(x-d)=0$$ are?