1. The problem is to evaluate the expression $i^{100}$, where $i$ is the imaginary unit with the property $i^2 = -1$. 2. Recall the powers of $i$ cycle every 4 steps: - $i^1 = i$ - $i^2 = -1$ - $i^3 = -i$ - $i^4 = 1$ 3. To find $i^{100}$, we reduce the exponent modulo 4: $$100 \mod 4 = 0$$ 4. Since the remainder is 0, $i^{100} = i^{4 \times 25} = (i^4)^{25} = 1^{25} = 1$. 5. Therefore, the value of $i^{100}$ is $1$.