To simplify the power of i (the imaginary unit), we need to know that i has a cycle:

i^1 = i,
i^2 = -1,
i^3 = -i,
i^4 = 1,
and then it repeats.

So, to simplify i^33, we need to find the remainder when 33 is divided by 4 (because i has a cycle of 4).

33 divided by 4 is 8 remainder 1.

So, i^33 is the same as i^1, which is simply i.

So, i^33 simplifies to i.

Question

To simplify the power of i (the imaginary unit), we need to know that i has a cycle:

i^1 = i,
i^2 = -1,
i^3 = -i,
i^4 = 1,
and then it repeats.

So, to simplify i^33, we need to find the remainder when 33 is divided by 4 (because i has a cycle of 4).

33 divided by 4 is 8 remainder 1.

So, i^33 is the same as i^1, which is simply i.

So, i^33 simplifies to i.

Knowee AI · Accepted Answer

To simplify the power of i (the imaginary unit), we need to know that i has a cycle:

i^1 = i,
i^2 = -1,
i^3 = -i,
i^4 = 1,
and then it repeats.

So, to simplify i^33, we need to find the remainder when 33 is divided by 4 (because i has a cycle of 4).

33 divided by 4 is 8 remainder 1.

So, i^33 is the same as i^1, which is simply i.

So, i^33 simplifies to i.

Simplify the power of i.i33