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Math Help - Complex number with De Moivre's formula

  1. #1
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    Complex number with De Moivre's formula

    don't know where should i post this.

    Find the real part of the complex number (i-1)^3 by using De Moivre's formula


    My lecture notes is too brief need help !

    thanks ")
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  2. #2
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    Write it in the polar form:

    \displaystyle (i-1)^3 = \bigg[\sqrt{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\si  n\left(\frac{3\pi}{4}\right)\right)\bigg]^3.

    De Moivre's theorem tells you that, for any arbitrary x and integer n, we have:

    \left(\cos{x}+i\sin{x}\right)^n = \cos\left(nx\right)+i\sin\left(nx\right).
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  3. #3
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    Expand \left( { - 1 + i} \right)^3  = \sum\limits_{k = 0}^3 {\dbinom{3}{k}\left( { - 1} \right)^{3 - k} \left( i \right)^k }.
    The real parts occur when k=0~\&~2.
    What do they add up to?
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