SOLUTION: i^2 is then (-1) 1. what is i^3? 2. what is (i-1)(i+1)? 3. what is i^4? 4. What is i^n is n is an even number? and if n is an odd number?

Algebra ->  Radicals -> SOLUTION: i^2 is then (-1) 1. what is i^3? 2. what is (i-1)(i+1)? 3. what is i^4? 4. What is i^n is n is an even number? and if n is an odd number?      Log On


   



Question 324178: i^2 is then (-1)
1. what is i^3?
2. what is (i-1)(i+1)?
3. what is i^4?
4. What is i^n is n is an even number? and if n is an odd number?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
i^2 is then (-1)
1. what is i^3?
i%5E3+=+i%5E2%2Ai
= -i
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2. what is (i-1)(i+1)?
= i%5E2+-+1+=+-1-1
= -2
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3. what is i^4?
i%5E4+=+%28i%5E2%29%5E2+=+%28-1%29%5E2
= 1
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4. What is i^n is n is an even number?
It's either -1 or +1.
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and if n is an odd number?
Either -i or +i
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Odd or even is not sufficient to specify the result. It's a modulo 4 function.
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i^n = i to the power of the remainder of n/4.