Ask Question
24 July, 17:26

Simplify i22. possible choices are 1, - 1, i,-i

+1
Answers (2)
  1. 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.
  2. 24 July, 20:26
    0
    The answer to this question is 1
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Simplify i22. possible choices are 1, - 1, i,-i ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers