# Thread: Eliminating Imaginary Numbers from a Denominator

1. ## Eliminating Imaginary Numbers from a Denominator

I need to eliminate the imaginary numbers from the denominator of the following equation and I have no idea where to start.

3/(s+2-2i)

2. Originally Posted by afn2
I need to eliminate the imaginary numbers from the denominator of the following equation and I have no idea where to start.

3/(s+2-2i)

You multiply by the conjuage
$\displaystyle \frac{3}{(s+2)-2i} \cdot \frac{(s+2)+2i}{(s+2)+2i}$
Thus,
$\displaystyle \frac{3(s+2)+3(2i)}{(s+2)^2-4i^2}$
Thus,
$\displaystyle \frac{3s+6+6i}{s^2+4s+8}$

3. Originally Posted by afn2
I need to eliminate the imaginary numbers from the denominator of the following equation and I have no idea where to start.

3/(s+2-2i)

$\displaystyle \frac{3}{2+\sqrt{5}}$
$\displaystyle \frac{3}{2+i} = \frac{3}{2+\sqrt{-1}}$
In each case the denominator takes the form $\displaystyle a+\sqrt{b}$ and you need to multiply the denominator by $\displaystyle a-\sqrt{b}$ to remove the square root.