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

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

Mathematics
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hint: we can write this: \[\Large 1 + i = \sqrt 2 {e^{i\pi /4}}\]
Forgot to note: This question is supposed to be for Algebra II level math, I don't recall using that when I did it
sorry!

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Other answers:

My mistake :)
sincerely I don't know how to get the requested value without using the polar form of a complex number
That's alright, thank you anyway
ok! :)
|dw:1439160808076:dw|
will that work for you?
another possible way is to use the binomial theorem of Newton, or the triangle of Tartaglia
Thank you both for the help, triciaal for the Algebra II way and Michele_Laino for the more advanced concepts (:
:)
you are welcome
@Michele_Laino what is the triangle of Tartaglia? never heard of it. Is it the same as Pascal's Triangle?
yes! I think so the triangle of Tartaglia is: 1 1 1 1 2 1 1 3 3 1 and so on...
Thanks yes Pascal's Triangle and Pascal was before Newton.
:)

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