Complex Numbers...

Let $$\displaystyle \left| Z_{r}-r\right| \leq r,\forall r=1,2,3,.......n.$$ Then $$\displaystyle \left| \sum_{r=1}^{n} Z_{r} \right| $$ is less than

The number of real roots of the equation $$\displaystyle \frac{A^{2}}{x} +\frac{B^{2}}{x-1}=1$$ where A and B are real numbers not equal to zero simultaneously, is :

Number of complex numbers $$z$$ satisfying $$\left| 2z \right| =\left| 2z-1 \right| =\left| 2z+1 \right| $$ is equal to-

If both a and b belong to the set $$\displaystyle \left\{ 1,2,3,4 \right\}$$ then the number of equations of the form $$ ax^{2}+bx+1=0$$ having real roots is :

If 0 $$\leq$$ argz $$\leq \displaystyle \frac{\pi}{4}$$, then the least value of $$\sqrt 2 |2z - 4|$$ is

If $$\displaystyle z= (i)^{(i)^{(i)}}$$ where $$ i = \sqrt{-1}$$, then $$z$$ is equal to

If the equation $$\displaystyle 16x^{2}+6kx+4=0$$ has equal roots, then the value of $$k$$ is 

The roots of the equations $$\displaystyle x^{2}-x-3=0$$ are

The quadratic equation $$ax^{2}+bx+c=0$$ will always have imaginary roots if:

Which of the following equation has two equal real toots ?