Question

Simplify i^{38}
i
-1
-i
1

Answer 1

Alright lets do this together.. first what do you think the answer is @Tatsurion

Answer 2

1 is my guess.

Answer 3

I believe you are right. You might want to confirm with someone else though :)

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Answer 4

Have a great day!

Answer 5

Says it's -1. https://mathway.com/popular-problems/Algebra/201886

Answer 6

there is a simple way to figure those

when you keep adding another i power a few times, you will notice a cycle every 4 terms repeat.

so you can divide that large number by 4, and figure where in that 4 term sequence the anser is

Answer 7

i = i
i^2 = -1
i^3 = i^2*i = -i
i^4 = +1

then it repeats again, , like i^5 is just i^4 *i = i, same as i^1

Answer 8

So it is 1?

Answer 9

since that cycle repeats, you can take all the 4's out of 38, and the remainder will be the term in that 4 term sequence to use


4 goes into 38, 9 times, left over with 2 reaining, must be the same as i^2, the second of the 4 terms

Answer 10

-1

Answer 11

Oh! Now I get it.

Answer 12

or maybe think of it as, i^4 is just 1

factor out all the i^4 you can , those go to just multiplying by 1, left with the same answer