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Math Help - Diving complex numbers

  1. #1
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    Diving complex numbers

    How would I divide
     1/<br />
1+i - 1/1-i
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by colerelm1 View Post
    How would I divide
     1/<br />
1+i - 1/1-i
    Do you mean \dfrac{1}{1+i}-\dfrac{1}{1-i}?

    First combine the two fractions by getting a common denominator: \dfrac{1}{1+i}-\dfrac{1}{1-i}=\dfrac{(1-i)-(1+i)}{(1+i)(1-i)}=\ldots.

    Can you finish the problem?
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  3. #3
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    Well I had actually already gotten that far....I just dont know what I should do right after that step.
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  4. #4
    MHF Contributor harish21's Avatar
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    if you got that far, you should know that it becomes:

    \dfrac{(1-i)-(1+i)}{(1+i)(1-i)}= \dfrac{1-i-1-i}{(1)^{2}-(i)^{2}}

    what is i^2?
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  5. #5
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    Here is suggestion on a different way to approach this sort of problem.

    Recall that \dfrac{1}{z} = \dfrac{{\overline z }}{{\left| z \right|^2 }}.

    So \dfrac{1}{{1 + i}} - \dfrac{1}{{1 - i}} becomes  \dfrac{{1 - i}}{2} - \dfrac{{1 + i}}{2} which is easier to deal with.
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