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Math Help - simplify equation

  1. #1
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    simplify equation

    Hi guys
    i am trying to solve some math questions for fun and i faced a problem
    the question says simplify the following equation :
    3-2i/3+2i
    can you please help me to simplify it
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  2. #2
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    Multiply both the top and bottom with the denominator's conjugate:

     \frac{3-2i}{3+2i} \times \frac{3-2i}{3-2i}
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  3. #3
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    I tried but no real simplification happens
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  4. #4
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    It's simplified because you end up with one complex number, instead of a complex number divided by another. This makes it easier to use this expression to solve complex number problems.
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  5. #5
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    can you please show me how to do it please because i couldont do it
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  6. #6
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    \frac{3-2i}{3+2i} \times \frac{3-2i}{3-2i}

    = \frac{9 - 6i - 6i + 4i^2}{9 -6i + 6i - 4i^2}

     = \frac{9 + 4(-1) - 12i}{9-4(-1)}

     = \frac{5 - 12i}{13}= \frac{5}{13} - \frac{12i}{13}
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  7. #7
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    Thank you very much ,, i forgot that i^2=-1
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