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

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

a. is correct