Question

simplify each of the following powers of i.
$i^{15}=-i$ (marked as complete)
$i^{32}=$ (with multiple - choice options: i, -i, 1, -1)

Explanation:

Step1: Recall the pattern of powers of $i$

$i^1 = i$, $i^2=- 1$, $i^3 = i^2\times i=-i$, $i^4=(i^2)^2 = 1$. The powers of $i$ repeat every 4.

Step2: Divide the exponent by 4

For $i^{32}$, divide 32 by 4: $32\div4 = 8$ with a remainder of 0.

Step3: Determine the value

When the remainder is 0 after dividing the exponent of $i$ by 4, the value of $i^n$ is 1. So $i^{32}=1$.

Answer:

1