Question

Simplify i^12 A. -1 B. -i C. i D. 1

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

Answer:

D. 1.

Step-by-step explanation:

We know that the powers of the imaginary constant, i, follow a certain pattern.

i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1.

Every 4 powers, the result cycles back to the original i. This is because there are only 4 unique digits that result from raising i to various powers.

To figure a higher power, such as 12, we need to take the remainder of the power when divided by 4 (the amount of unique answers), to simplify it to the original 4 powers.

So when you have i^12 power, the remainder is 0. This is because 4 is a factor of 12. As a result, we can simplify this to i^8, and therefore i^4, which equals 1.

I hope this helps!