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Math Help - Euler form

  1. #1
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    Euler form

    Hi,

    Q1. Simplify the following, working by hand Give the answers in the form a+bi with a and b exact real numbers, not decimal approximations.

    [squareroot(2) - i*squareroot(2)]^10 (use euler form)


    I would like answer and steps please.
    If there is anything unclear, let me know, thanks in advance.
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  2. #2
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    Quote Originally Posted by Moon Hoplite View Post
    Hi,

    Q1. Simplify the following, working by hand Give the answers in the form a+bi with a and b exact real numbers, not decimal approximations.

    [squareroot(2) - i*squareroot(2)]^10 (use euler form)


    I would like answer and steps please.
    If there is anything unclear, let me know, thanks in advance.
     = (\sqrt{2})^{10} (1 - i)^{10}.

    Convert 1 - i to polar form and get (1 - i)^{10} using de Moivre's theorem. Then convert the result into Cartesian form.
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