Question

score: 1/5 penalty: 0.25 off
question
evaluate:
$i^{54}$
answer
$\bigcirc$ 1 $\bigcirc$ $-1$
$\bigcirc$ $i$ $\bigcirc$ $-i$

Explanation:

Step1: Find remainder of exponent mod 4

$54 \div 4 = 13$ remainder $2$, so $54 = 4\times13 + 2$

Step2: Simplify using $i^4=1$

$i^{54} = i^{4\times13 + 2} = (i^4)^{13} \times i^2 = 1^{13} \times i^2$

Step3: Substitute $i^2=-1$

$1^{13} \times (-1) = -1$

Answer:

$-1$