+8 Find the number integer values of n so that (n + 2i)^4 is an integer.
+128407 (n + 2i)^4 =
n^4 + 4n^3 * 2i + 6n^2 * (2i)^2 + 4n (2i)^3 + (2i)^4 =
n^4 + 8n^3 i + 24n^2 i^2 + 32n i^3 + 16i^4 =
n^4 + 8n^3 i - 24n^2 - 32n i + 16
The terms in red will always be integers for any integer n
So
8n^3 i - 32n i = 0 ( we want to eliminate the "i's" )
8n i ( n^2 - 4) = 0
8n i ( n + 2) ( n - 2) = 0
This will be true when n = 0 n = -2 and n = 2
