Question

Chose a power of
i
(with an exponent 13 or higher) that is equivalent to : i^3

3
. Explain how you arrived at your answer.

Answer 1

To find a power of i that is equivalent to i^3, we can start by calculating the value of i^3 first.

Using the formula for powers of i, where i^2 = -1, we can simplify i^3 as follows:

i^3 = (i^2) * i
= (-1) * i
= -i

Now, we need to find a power of i with an exponent 13 or higher that is equivalent to -i.

If we multiply i by itself 4 times, we get:

i^4 = (i^2)^2
= (-1)^2
= 1

Therefore, i^4 is equal to 1.

Since i^3 = -i, we can simplify i^3 * i = -i * i = -i^2.

Using the value of i^4 = 1, we can substitute -i^2 as follows:

-i^2 = -1 * (i^2)
= -1 * 1
= -1

Therefore, i^3 * i = -1.

Hence, a power of i (with an exponent 13 or higher) that is equivalent to i^3 is -1.