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Mathematics
Guest
24 July, 17:26
Simplify i22. possible choices are 1, - 1, i,-i
+1
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Dillan West
24 July, 19:30
0
I assume you mean i^22
There’s a cycle i follows when being taken to a certain power, so let’s see what that is:
i^1 = i
i^2 = - 1
i^3 = - i
i^4 = 1
And i^5 = i, so our cycle repeats after every 4th power. To find i^22 then, we can divide 22 by 4 to obtain an answer of 5, with a remainder of 2. In other words, 22 = 4 (5) + 2
So, i^22 = i^[4 (5) + 2]
We can break that up into the product i^[4 (5) ] x i^2
We know that i^4 is 1, and 1^5 is still 1, so i^[4 (5) ] = 1; i^2 is simply - 1, so altogether, we find that
i^[4 (5) ] x i^2 = 1 x (-1) = - 1
Our answer then is - 1.
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Josephine Madden
24 July, 20:26
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The answer to this question is 1
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