Posted by **car** on Tuesday, January 18, 2011 at 9:08am.

Is i^2=-1 for how many integers N is (N+i)^4 an integer?

so far i have factored out (N+i)^4 to be ... n^4+2n^2+1 i would suggest checking that, but from there i don't know where to go...doesn't it work for every integer?

- Math -
**Reiny**, Tuesday, January 18, 2011 at 9:37am
first of all

(N+1)^4 = N^4 + 4N^3(i) + 6N^2(i^2) + 4N(i^3) + i^4

= N^4 + 4N^3(i) - 6N^2 - 4N(i) + 1

= N^4 + 4i(N^3 -N) + 1

for this to be an integer, the i-term must drop out, that is, N^3 - N = 0

N(N^2 - 1) = 0

N(N+1)(N-1) = 0

N = 0, -1, or +1

check my arithmetic

## Answer This Question

## Related Questions

- algebra1 - Find to consecutive integers that the sum of 3 times the first ...
- math - there are 8 consecutive integers that add up to 31. Only two of the ...
- math, algebra - 2a+2ab+2b I need a lot of help in this one. it says find two ...
- Math - x^2+x-k find all positive values for k, if it can be factored Allowed ...
- Integer math - Find 7 A)1/7 B)-7 C)7 D)0 Find -14 A)14 B)-14 C)1/14 D)0 If two ...
- math - what is the expression for the factored form of 1/4y^2-36? I got (1/4y-6...
- math - Using these integers:-1,+6,-8,+3,-2 a) Which integers have the greatest ...
- PROGRAMMING - 1. Make a C program that will input two integers and then to enter...
- math 117 - If one half of one integer is subtracted from three fifths of the ...
- algebra - For three consecutive odd integers, the sum of 3 times the ...

More Related Questions