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    krdiggs's Avatar
    krdiggs Posts: 2, Reputation: 1
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    #1

    Jul 27, 2010, 12:59 PM
    Can you help answer how this problem is solved?
    Can you help answer how this problem is solved?Express in a + bi form... (2 - 2i) ^5 ?

    The answer is -128 + 128i... but how?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Jul 27, 2010, 01:32 PM

    Two ways to do this:

    1) Brute foirce, using a polynomial expansion:



    Apply this to (2-2i), and you get



    2) Use D'Moivre's theorem:


    where


    Convert 2-2i to polar cordinates for the cis form: (2-2i) is radius 2 and angle



    Finally, convert back to rectangular coordinates:


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