Answer:
The answer can be i^4 , i^32 , i^124
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