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Math Help - Powers of complex numbers

  1. #1
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    Powers of complex numbers

    Evaluate (2 + 2i)^8
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  2. #2
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    Hello adam456006
    Quote Originally Posted by adam456006 View Post
    Evaluate (2 + 2i)^8
    Note that (1+i)^2 = 1 +2i + i^2 = 2i and that (2+2i)^8 = 2^8(1+i)^8. Can you do it now?

    (The answer is 2^{12}.)

    Grandad
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  3. #3
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    Talking

    Quote Originally Posted by adam456006 View Post
    Evaluate (2 + 2i)^8
    Have you studied the Binomial Theorem at all? Because that might be a "nicer" way to go, rather than doing all the multiplications by hand.

    What have you tried? How far have you gotten? Where are you stuck?

    Please be complete. Thank you!
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  4. #4
    Senior Member Twig's Avatar
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    Also, you could write z=2+2i as
    z= \sqrt{8}(cos(\frac{\pi}{4}) + i \, sin(\frac{\pi}{4}))

    So you get  z^{8}=8^{4} = 2^{12}
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