Ask Question
27 January, 05:06

Give three answers that are equivalent to the expression: i^ 1012

+5
Answers (1)
  1. 27 January, 08:08
    0
    The answer can be i^4, i^32, i^124

    Step-by-step explanation:

    * Lets explain the the imaginary number i

    - The number i is an imaginary number because its value is √ (-1)

    ∵ i = √ (-1)

    ∴ i² = - 1

    ∴ i³ = - i

    ∴ i^4 = 1

    ∴ i^5 = i and so on

    - Then if you want to know i^n = ?, you must to check n

    # If n is an even number divisible by 4 then the answer is 1

    # If n is an even number not divisible by 4 then the answer is - 1

    - Ex: i^16 = 1 but i^26 = - 1

    # If n is an odd number, then the answer will be i or - i, to know check

    n - 1 if it divisible by 4, then the answer is i if not divisible by 4, then

    the answer is - i

    - Ex: i^13 = i, but i^15 = - i

    * Now lets solve the problem

    ∵ The expression is i^1012

    ∵ 1012 is an even number and divisible by 4

    ∴ i^1012 = 1

    ∴ The answer can be i^4, i^32, i^124
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “Give three answers that are equivalent to the expression: i^ 1012 ...” 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