# Eliminating Imaginary Numbers from a Denominator

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• 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)

Please help!
• 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)

Please help!

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)

Please help!

It may help to consider this as a similar method (the exact same, actually) as another you've doubtless run into: rationalizing the denominator. Consider the similarities in the two following "simplification" problems.
$\frac{3}{2+\sqrt{5}}$

and
$\frac{3}{2+i} = \frac{3}{2+\sqrt{-1}}$

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.

-Dan
• Aug 31st 2006, 08:48 AM
afn2
THANKS a MILLION for the help guys. I had been reading help hints on the internet all day, but wasn't really getting what they were trying to say, so this really helped!