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

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

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

Postby AmySaunders on 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?
AmySaunders
 
Posts: 34
Joined: Thu Aug 20, 2009 6:27 pm

Sponsor

Sponsor
 

  TOPIC_SOLVED

Postby stapel_eliz on 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:
User avatar
stapel_eliz
 
Posts: 1717
Joined: Mon Dec 08, 2008 4:22 pm

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

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

You are right, I wasn't thinking.
AmySaunders
 
Posts: 34
Joined: Thu Aug 20, 2009 6:27 pm

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

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

So the answer would be 2^50?
AmySaunders
 
Posts: 34
Joined: Thu Aug 20, 2009 6:27 pm

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

Postby nona.m.nona on 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.
nona.m.nona
 
Posts: 254
Joined: Sun Dec 14, 2008 11:07 pm


Return to Advanced Algebra ("pre-calculus")