i cubed = real number?

Discussion in 'Math' started by strantor, Oct 7, 2012.

  1. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    I'm doing online homework, and the question is
    The correct answers, verified by the system, are:
    {-8, 4-4\sqrt{3}i, 4+4\sqrt{3}i}

    I don't understand how the last 2 are correct, because i X i = -1, so (4+4\sqrt{3}i ) * (4+4\sqrt{3}i ) should be a real number, but (4+4\sqrt{3}i ) * (4+4\sqrt{3}i ) * (4+4\sqrt{3}i )should be an imaginary number, correct?
     
  2. Papabravo

    Expert

    Feb 24, 2006
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    Wrong. Multiply it out and see how the terms with the imaginary unit cancel each other out.
     
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  3. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    DOH! Yep, they sure do.
    Thanks

    EDIT:
    I was also wrong about (4+4\sqrt{3}i ) * (4+4\sqrt{3}i ) being a real number.
     
  4. Papabravo

    Expert

    Feb 24, 2006
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    No sweat. We all have occasional lapses where our intuition plays tricks on us.
     
  5. WBahn

    Moderator

    Mar 31, 2012
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    Just want to chime and say that it's good to see someone asking "does the answer make sense?", and that includes asking it of the "book's" answers, since the book will be wrong from ime to time.
     
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