SOLUTION: Calculate the first 10 powers of i. Observe the pattern. Explain how to quickly calculate any whole number power of i.( ex. What is i^312?)
I know how to calculate the first ten p
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-> SOLUTION: Calculate the first 10 powers of i. Observe the pattern. Explain how to quickly calculate any whole number power of i.( ex. What is i^312?)
I know how to calculate the first ten p
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Question 121401: Calculate the first 10 powers of i. Observe the pattern. Explain how to quickly calculate any whole number power of i.( ex. What is i^312?)
I know how to calculate the first ten powers and I see the pattern but I am awful at explaining to other people. Can you help? Found 2 solutions by stanbon, checkley71:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Since every 4th power is "1",
If you have i^x and x = 4k+r
the i^x = i^r
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Example: i^37 = i^(4*9+1) = i^1 = i
i^23 = i^(5*4+3) = i^3 = -i
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Cheers,
Stan H.
You can put this solution on YOUR website! i^1=sqrt-1
i^2=-1
i^3=1sqrt-1
i^4=1
i^5=1sqrt-1
i^6=-1
i^7=-1sqrt-1
i^8=1
i^9=1sqrt-1
i^10=-1
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i^312=i^(78*4) or i^4=1
IF THE POWER IS DIVISABLE BY 4 THEN THE ANSWER IS (1)
IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 1 THEN THE ANSWER IS (SQRT-1)
IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 2 THEN THE ANSWER IS (-1)
IF DIVIDING THE POWER BY 4 GIVES A REMAINDER OF 3 THEN THE ANSWER IS (1SQRT-1)
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