Let n be a positive integer. Find the number of distinct possible values of i^n + i^(-n). Note: i^2 = -1.
Method: Start by checking the different values, until you hit a pattern!
I'll just show it to you, the pattern repeats every four
i^1 = i
i^2 = -1
i^3 = -i because (-1*i)
i^4 = 1 because (-1*-1)
And after this it repeats as x * 1 = x
for the negatives,
i^-1 = -i
i^-2 = -1
i^-3 = i
i^-4 = 1
this repeats for the same reason.
I could let you finish the problem from here but this is webcalc you're here for the answers :)
1: i + -i = 0
2: -1 + -1 = -2
3: -i + i = 0 (again)
4: 1 + 1 = 2 (my favorite expression of all time :D )
the total answers aare 0 -2 and 2, so your answer is : 3