Question 3(Multiple Choice Worth 2 points) (01.06 MC) Simplify r^31 1 -1 i -i

## Step 1: Simplify using powers of $i$<br />### We know that $i^1 = i$, $i^2 = -1$, $i^3 = -i$, and $i^4 = 1$. These powers of $i$ repeat in a cycle of 4. To simplify $i^{31}$, we can find the remainder when 31 is divided by 4.<br />## Step 2: Finding the remainder<br />### $31 \div 4 = 7$ with a remainder of 3. This means $i^{31} = i^{4 \times 7 + 3} = (i^4)^7 \times i^3 = 1^7 \times i^3 = 1 \times i^3 = i^3$.<br />## Step 3: Substituting the value of $i^3$<br />### Since $i^3 = -i$, we have $i^{31} = -i$.