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Let n be a positive integer.  Find the number of distinct possible values of i^n + i^(-n).  Note: i^2 = -1.

 May 9, 2020
 #1
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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 :)

 

Diff values:
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

 May 9, 2020

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