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Math Help - Find the smallest integer

  1. #1
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    Find the smallest integer

    Find the smallest integer n for which (1+i/1-i)^n=1
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  2. #2
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    Hello,
    Quote Originally Posted by varunnayudu View Post
    Find the smallest integer n for which (1+i/1-i)^n=1
    1+i=\sqrt{2} e^{i \frac{\pi}{4}}
    1-i=\sqrt{2} e^{-i\frac{\pi}{4}}

    So \frac{1+i}{1-i}=e^{i \frac{\pi}{2}}=i

    Hence \left(\frac{1+i}{1-i}\right)^n=i^n
    n=0
    or n=4
    etc...
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  3. #3
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    Where to find a complete explanation for this

    Thanks for ur reply but please can u tell me from where have u gottten this from, i need it as a reference. If u could please recommend me a book from which i can refer this from.
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  4. #4
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    Hmm I don't know any reference in English.

    I used this formula :
    a+ib=\sqrt{a^2+b^2} \cdot e^{i \arctan \frac ab}

    then use the properties of i :
    i^2=-1
    then i^4=1
    etc..

    http://en.wikipedia.org/wiki/Complex...the_polar_form
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