Number Theory T...

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

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

If $$z = \dfrac {(\sqrt {3} + i)^{3} (3i + 4)^{2}}{(8 + 6i)^{2}}$$, then $$|z|$$ is equal to

The value of $$(a+2i)(b-i)$$ is

The expression $$\dfrac{3-4i}{5+3i}$$ is equivalent to

The fraction $$\dfrac{1}{1+i}$$ is equivalent to

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

Perform the indicated operations:
$$(5+3i)(3-2i)$$

If $$x + i  y = \dfrac{3}{2 + cos  \theta + i  sin  \theta}$$, then $$x^2 + y^2$$ is equal to

Let $$z = x + iy$$, where $$x$$ and $$y$$ are real. The points $$(x, y)$$ in the $$X-Y$$ plane for which $$\dfrac {z + i}{z - i}$$ is purely imaginary lie on