Complex Numbers...

The value of $$(x - 1) \displaystyle \left ( x + \frac{1}{2} - \frac{\sqrt{3}}{2} i \right )\left ( x + \frac{1}{2} + \frac{\sqrt 3}{2} i \right )$$ is

The number of real solutions of the equation $$\displaystyle{\left(\frac{5}{7}\right)^2}=-x^2+2x-3$$ is equal to 

Number of integer values of k for which the quadratic equation $$\displaystyle 2x^{2}+kx-4=0$$ will have two rational solutions is

If $$z_1$$ and $$z_2$$ are any two complex numbers, then $$\displaystyle \frac{z_2 + z_1}{||z_2| - |z_1||}$$ is

Find the value of $$k$$ for which the quadratic equation $$\displaystyle \left ( k-2 \right )x^{2}+2\left ( 2k-3 \right )x+5k-6=0$$ has equal roots

The locus represented by $$|z -1|=|z + i|$$ is

If the roots of the equation $$\displaystyle \left ( a^{2}+b^{2} \right )x^{2}-2b\left ( a+c \right )x+\left ( b^{2}+c^{2} \right )=0 $$ are equal then

In the argand diagram, if $$O,P$$ and $$Q$$ represents respectively the origin and the complex numbers $$z$$ and $$z+iz$$ then the $$\angle OPQ$$ is

The value (s) of $$k$$ for which the quadratic equation $$\displaystyle kx^{2}-kx+1=0$$ has equal roots is

Let $$z = x + iy$$ & amp $$(e^{z^2})$$ = amp $$(e^{(z+i)})$$. If $$y = (x)$$ is a function, then $$y(3)$$ is equal to