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anonymous

  • one year ago

Solve (i+1)^21 without a calculator. I know the answer, but forgot how to do it.

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  1. Michele_Laino
    • one year ago
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    hint: we can write this: \[\Large 1 + i = \sqrt 2 {e^{i\pi /4}}\]

  2. anonymous
    • one year ago
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    Forgot to note: This question is supposed to be for Algebra II level math, I don't recall using that when I did it

  3. Michele_Laino
    • one year ago
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    sorry!

  4. anonymous
    • one year ago
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    My mistake :)

  5. Michele_Laino
    • one year ago
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    sincerely I don't know how to get the requested value without using the polar form of a complex number

  6. anonymous
    • one year ago
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    That's alright, thank you anyway

  7. Michele_Laino
    • one year ago
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    ok! :)

  8. triciaal
    • one year ago
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    |dw:1439160808076:dw|

  9. triciaal
    • one year ago
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    will that work for you?

  10. Michele_Laino
    • one year ago
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    another possible way is to use the binomial theorem of Newton, or the triangle of Tartaglia

  11. anonymous
    • one year ago
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    Thank you both for the help, triciaal for the Algebra II way and Michele_Laino for the more advanced concepts (:

  12. Michele_Laino
    • one year ago
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    :)

  13. triciaal
    • one year ago
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    you are welcome

  14. triciaal
    • one year ago
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    @Michele_Laino what is the triangle of Tartaglia? never heard of it. Is it the same as Pascal's Triangle?

  15. Michele_Laino
    • one year ago
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    yes! I think so the triangle of Tartaglia is: 1 1 1 1 2 1 1 3 3 1 and so on...

  16. triciaal
    • one year ago
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    Thanks yes Pascal's Triangle and Pascal was before Newton.

  17. Michele_Laino
    • one year ago
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    :)

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