SOLUTION: the expression i^42 is equivalent to?

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Question 394183: the expression i^42 is equivalent to?
Found 2 solutions by Edwin McCravy, CharlesG2:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
the expression i42 is equivalent to ?


You need to know these three facts:

i2 = -1

(-1)EVEN = +1

(-1)ODD = -1

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Your example:

i42 = i2*21 = (i2)21 = (-1)21 = -1

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Some other examples:

i96 = i2*48 = (i2)48 = (-1)48 = +1 = 1

i73 = i72+1 = i72i1 = i2*36i = (i2)36i = (-1)36i = 1i = i

i47 = i46+1 = i46i1 = i2*23i = (12)23i = (-1)23i = (-1)i = -i

Edwin

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
the expression i^42 is equivalent to?

i = sqrt(-1)
i^2 = -1
i^4 = 1
i^8 = 1
i^16 = 1
i^32 = 1
i^36 = 1
i^40 = 1
i^41 = i
i^42 = i^2 = -1
every multiple of 4 on the exponent is equal to 1