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

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
AmySaunders
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Joined: Thu Aug 20, 2009 6:27 pm
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### imaginary numbers? value of (1 + i)^100

(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
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(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
Posts: 34
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### Re: imaginary numbers? value of (1 + i)^100

You are right, I wasn't thinking.

AmySaunders
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### Re: imaginary numbers? value of (1 + i)^100

So the answer would be 2^50?

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
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### Re: imaginary numbers? value of (1 + i)^100

So the answer would be 2^50?