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

1. Michele_Laino

hint: we can write this: $\Large 1 + i = \sqrt 2 {e^{i\pi /4}}$

2. anonymous

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

sorry!

4. anonymous

My mistake :)

5. Michele_Laino

sincerely I don't know how to get the requested value without using the polar form of a complex number

6. anonymous

That's alright, thank you anyway

7. Michele_Laino

ok! :)

8. triciaal

|dw:1439160808076:dw|

9. triciaal

will that work for you?

10. Michele_Laino

another possible way is to use the binomial theorem of Newton, or the triangle of Tartaglia

11. anonymous

Thank you both for the help, triciaal for the Algebra II way and Michele_Laino for the more advanced concepts (:

12. Michele_Laino

:)

13. triciaal

you are welcome

14. triciaal

@Michele_Laino what is the triangle of Tartaglia? never heard of it. Is it the same as Pascal's Triangle?

15. Michele_Laino

yes! I think so the triangle of Tartaglia is: 1 1 1 1 2 1 1 3 3 1 and so on...

16. triciaal

Thanks yes Pascal's Triangle and Pascal was before Newton.

17. Michele_Laino

:)