Complex Numbers...

The values of $$b$$ for which the equation $$\displaystyle { 2bx }^{ 2 }-40x+25=0$$ has equal root is :

If $$z_1, z_2$$ and $$z_3$$ are complex numbers such that $$|z_1| = |z_2| = |z_3| = \left | \displaystyle \frac{1}{z_1} + \frac{1}{z_2} + \frac{1}{z_3} \right | = 1,$$ then $$|z_1 + z_2 + z_3|$$ is

For what values of k, will quadratic equation $$\displaystyle { 9x }^{ 2 }+3kx+4=0$$ have real and equal roots? 

Find the value of P for which the following equation has equal roots $$\displaystyle { px }^{ 2 }-8x+2p=0$$ 

Which of the following equations has no solution for $$a$$ ?

The roots of the equation $${2x^{2 }+ 3x + 2} = 0$$ are

Let $${ X }_{ n }=\left\{ z=x+iy:{ \left| z \right|  }^{ 2 } \le \dfrac { 1 }{ n }  \right\} $$ for all integers $$n\ge 1$$. Then, $$\displaystyle\bigcap _{ n=1 }^{ \infty  }{ { X }_{ n } } $$ is

The modulus of $$\dfrac { 1-i }{ 3+i } +\dfrac { 4i }{ 5 } $$ is

In the complex numbers, where $$i = \sqrt {-1}$$, the conjugate of any value $$a + bi$$ is $$a -ib$$. What is the result when you multiply $$2 + 7i$$ by its conjugate?

In the complex numbers, where $$i^{2} = -1$$, what is the value of $$5 + 6i$$ multiplied by $$3-  2i$$?