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Math Help - Product of complex numbers.

  1. #1
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    Product of complex numbers.

    I am having trouble simplifying this: (-5+3i)^2



    and I don't understand how to divide:
    (3-4i)/(5-2i)


    Any help would be great
    Last edited by mr fantastic; September 9th 2010 at 01:15 PM. Reason: Re-titled.
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by Joaco View Post
    I am having trouble simplifying this: (-5+3i)^2



    and I don't understand how to divide:
    (3-4i)/(5-2i)


    Any help would be great


    it's just as you wrote :

     (-5+3i)(-5+3i ) = 25-15i-15i-9 = 16-30i

    P.S. because  i^2 = -1


    and for that problem with dividing that two complex numbers ...

     \displaystyle \frac {3-4i}{5-2i}

    multiply now with ...

      \displaystyle \frac {3-4i}{5-2i} \cdot \frac {5+2i}{5+2i} = \frac {(3-4i)(5+2i)}{(5-2i)(5+2i)}

    can you continue ?
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  3. #3
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    Quote Originally Posted by Joaco View Post
    I am having trouble simplifying this: (-5+3i)^2



    and I don't understand how to divide:
    (3-4i)/(5-2i)


    Any help would be great
    For division, standard procedure is to multiply numerator and denominator by the conjugate of the denominator (thus making the denominator a real number).
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  4. #4
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    Learn this useful formula:  \displaystyle \frac{z}{w}=\frac{z\cdot \overline{w}}{|w|^2}.

    So  \displaystyle \frac{3-4i}{5-2i}=\frac{(3-4i)(5+2i)}{29}
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  5. #5
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    Quote Originally Posted by yeKciM View Post

    and for that problem with dividing that two complex numbers ...

     \displaystyle \frac {3-4i}{5-2i}

    multiply now with ...

      \displaystyle \frac {3-4i}{5-2i} \cdot \frac {5+2i}{5+2i} = \frac {(3-4i)(5+2i)}{(5-2i)(5+2i)}

    can you continue ?


    So it would be (23 - 14i)/ 29

    Quote Originally Posted by Plato View Post
    Learn this useful formula:  \displaystyle \frac{z}{w}=\frac{z\cdot \overline{w}}{|w|^2}.

    So  \displaystyle \frac{3-4i}{5-2i}=\frac{(3-4i)(5+2i)}{29}
    It makes a lot of sense




    Thank you everyone
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