Question

question
evaluate:
$i^{37}$
answer
$\bigcirc -1$
$\bigcirc i$
$\bigcirc -i$
$\bigcirc 1$

Explanation:

Step1: Use cyclicity of $i$

Recall that $i^4 = 1$, so we divide the exponent by 4 to find the remainder.
$37 \div 4 = 9$ with a remainder of 1, so $i^{37} = i^{4\times9 + 1}$

Step2: Simplify using exponent rules

$i^{4\times9 + 1} = (i^4)^9 \times i^1$
Since $i^4=1$, this becomes $1^9 \times i$

Step3: Compute final value

$1^9 = 1$, so $1 \times i = i$

Answer:

$\boldsymbol{i}$ (corresponding to the option: $\boldsymbol{i}$)