Complex Numbers...

Find $$(5 + 2i)(5 - 2i)$$

What is the smallest integral value of $$k$$ such that $$2x (kx - 4) - x^{2} + 6 = 0$$ has no real roots?

What can you say about the graph of $$y = x^{2} - 12x + 40$$?

For what value of 'p' are the roots of $$x^{2} - 5x = 2(3 + x) - 4p$$ real and equal?

Express  $$\dfrac {(-5-i)(-7+8i)}{(2-4i)}$$  in the form of a complex number $$a+bi$$.

If $$a, b, c$$ are real, what is the nature of the roots of the equation $$(a - x)(b - x) = c^{2}$$?

If $$(2 - i)\times(a - bi) = 2 + 9i$$, where i is the imaginary unit and a and b are real numbers, then a equals

What is the approximate magnitude of $$8 + 4i$$?

The real part of $${ \left( 1-\cos { \theta  } +i\sin { \theta  }  \right)  }^{ -1 }$$ is

The number of real roots of $$\left (x+\dfrac{1}{x}\right)^2-4=0$$ is