Question

Hey guys! Can you help me how to solve number 16, 18, and 20. Because I don’t understand how to solve this

Answer 1

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