imaginary numbers? value of (1 + i)^100

[AmySaunders]

(1+i)^100 equals which of the following quantities?
(a) 2^100
(b) -2^50
(c) 2^50
(d)1-2^100

I do know that i^2 is -1. so i^100=-1^50, right?
1^100=1.
So, 1-1^50 is what I come up with, and that is 0. Not an option. Can you tell me where I'm going wrong?

[stapel_eliz]

(1+i)^100 equals...

I do know that i^2 is -1. so i^100=-1^50, right?
1^100=1. So, 1-1^50 is what I come up with...

How are you getting that (1 + i)¹⁰⁰ equals 1¹⁰⁰ + i¹⁰⁰ ? Does that work for any other binomial?

[AmySaunders]

You are right, I wasn't thinking.

[AmySaunders]

So the answer would be 2^50?

[nona.m.nona]

So the answer would be 2^50?

What was your reasoning? What were your steps?

Please be complete. Thank you.