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Math Help - standard form

  1. #1
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    standard form

    please write (1 + i )^20 in standard form
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  2. #2
    MHF Contributor ebaines's Avatar
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    Use De Moivre's theorem: (r \cdot cis\theta )^n = r^n \cdot cis(n \theta) , where  cis(x) is defined as:  cis(x) = \cos(x) + i \sin(x) .

    Here (1+i) = \sqrt 2 cis(\frac {\pi} 4) so:

    <br />
(1+i)^{20} = (\sqrt 2)^{20} \cdot cis (20 \times \frac {\pi} 4 )= 2^{10} cis(5\pi) = 2^{10}(\cos(5\pi) + i \sin(5\pi)) = 2^{10}<br />
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