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

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

Postby AmySaunders » Tue Jan 18, 2011 5:44 pm

(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?

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stapel_eliz
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Postby stapel_eliz » Tue Jan 18, 2011 7:54 pm

AmySaunders wrote:(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? :confused:

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

Postby AmySaunders » Fri Mar 18, 2011 7:10 pm

You are right, I wasn't thinking.

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

Postby AmySaunders » Fri Mar 18, 2011 7:19 pm

So the answer would be 2^50?

nona.m.nona
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Re: imaginary numbers? value of (1 + i)^100

Postby nona.m.nona » Fri Mar 18, 2011 10:58 pm

AmySaunders wrote:So the answer would be 2^50?

What was your reasoning? What were your steps?

Please be complete. Thank you.


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