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Math Help - equate complex numbers

  1. #1
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    equate complex numbers

    Is it possible to solve for a and b in this equation?

    a+3b+(3a-b)i = 6+6i

    Just trying to help my son with his homework.

    Thanks for any information
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  2. #2
    Senior Member Stroodle's Avatar
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    Yes it is, as a+bi=c+di only if a=c and b=d

    So the two equations you have to solve simultaneously are:

    a+3b=6 and 3a-b=6
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  3. #3
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    Thanks I did get that far but was wondering where to go from there or is it something just done in my head.
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  4. #4
    Senior Member Stroodle's Avatar
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    If you rearrange the first equation you can see that a=6-3b, so now you can plug this value of a into the second equation, yielding 3(6-3b)-b=6

    Solving this gives b=\frac{6}{5}

    Now if you plug this value of b into either of the first two equations you can find the value of a
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  5. #5
    Senior Member Stroodle's Avatar
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    For more info on how to solve simultaneous equations you should have a look here Practical Algebra Lessons
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  6. #6
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    WOW!

    I actually think I understand it.

    Thanks so much
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