How do you simplify #i^922#?
1 Answer
Nov 21, 2015
Explanation:
If
#a^(m+n) = stackrel "m+n times" overbrace ((a)(a)...(a)) = stackrel "m times" overbrace ((a)(a)...(a)) stackrel "n times" overbrace ((a)(a)...(a)) = a^m*a^n#
Hence if
#(a^m)^n = stackrel "n times" overbrace ((a^m)(a^m)...(a^m)) = a^(stackrel "n times" overbrace (m+m+...+m)) = a^(mn)#
So:
#i^922 = i^(2*461) = (i^2)^461 = -1^(461) = (-1)^(2*230)(-1)^1#
#= ((-1)^2)^230(-1) = 1^230(-1) = -1#
