Complex Numbers...

The product of $$(3-2i)$$ and $$\left(\dfrac { 5 }{ 2 } -4i\right)$$, if $$i=\sqrt { -1 } $$ , is:

The resultant complex number when $$(4+6i)$$ is divided by $$(10-5i)$$ is

The argument of $$\dfrac {1 + i\sqrt {3}}{\sqrt {3} + i}$$ is

The principal amplitude of $$\displaystyle { \left( \sin { { 40 }^{ \circ  }+i\cos { { 40 }^{ \circ  } }  }  \right)  }^{ 5 }$$ is

If $$A = (3 - 4i)$$ and $$B = (9 + ki)$$, where $$k$$ is a constant. 

The simplest form of $$\sqrt {-18} \times \sqrt {-50}$$ is

Simplify $$(2+8i)(1-4i)-(3-2i)(6+4i)$$

Given that $$4$$ is a root of the quadratic equation $${x}^{2}-5x+q=0$$. Find the value of $$q$$ and the other root.

The imaginary number $$i$$ is defined such that $$i^2=-1$$. What is the value of $$(1 - i \sqrt {5}) ( 1 + i\sqrt {5})$$?

If $$i = \sqrt {-1}$$, find the values of $$n$$ such that $$i^{n} + (i)^{n}$$ have a positive value.