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-   -   Can you help answer how this problem is solved? (https://www.askmehelpdesk.com/showthread.php?t=492456)

  • Jul 27, 2010, 12:59 PM
    krdiggs
    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?
  • Jul 27, 2010, 01:32 PM
    ebaines

    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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