# Eliminating Imaginary Numbers from a Denominator

• Aug 31st 2006, 06:32 AM
afn2
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)

• Aug 31st 2006, 07:35 AM
ThePerfectHacker
Quote:

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
$\frac{3}{(s+2)-2i} \cdot \frac{(s+2)+2i}{(s+2)+2i}$
Thus,
$\frac{3(s+2)+3(2i)}{(s+2)^2-4i^2}$
Thus,
$\frac{3s+6+6i}{s^2+4s+8}$
• Aug 31st 2006, 07:41 AM
topsquark
Quote:

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)

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