Problem 16
Answer: i
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Work Shown:
The exponent 41 divided by 4 leads to
41/4 = 10 remainder 1
The "remainder 1" means that
i^(41) = i^1 = i
The reason why I divided by 4 is because the pattern shown below
i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
repeats itself over and over. So this is a block of four items repeated forever.
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Problem 18
Answer: 1
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Work Shown:
Divide 3136 over 4 to get
3136/4 = 784 remainder 0
Therefore,
i^3136 = i^0 = 1
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Problem 20
Answer: i
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Work Shown:
Combine i^6*i^7 into i^13. We add the exponents here
Now divide by 4 to find the remainder
13/4 = 3 remainder 1
So, i^13 = i^1 = i