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Math Help - Eliminating Imaginary Numbers from a Denominator

  1. #1
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    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!
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  2. #2
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    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}
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    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
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  4. #4
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    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!
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