11th grade math question, i^5 x 1^7 =

i^5 x 1^7 = ?

choices: 1, -1, i, -i

THANKS!

i^12 = (i^4)^3 = (+1)^3 =1

i ^ 12

(i ^ 4) ^ 3

1 ^ 3

1...........ANSWER

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i^5 x 1^7 = i^12

Powers of i form a repeating pattern............

i = √-1 = i
i^2 = - 1
i^3 = - i
i^4 = - i x i = 1
i^5 = i
i^6 = -1
i^7 = - i
i^8 = 1

You can see that the repeating sequence is i, -1, - i, 1, so you should be able to see what i^12 is....

(i^12 =1)

Since 1^7 equals 1, the answer is i^5

i * i = -1

So the answer is -i