Question

compute $i^{.608}$.

Explanation:

Step1: Recall the cycle of \(i\)

The imaginary unit \(i\) has a cyclic pattern: \(i^1 = i\), \(i^2 = -1\), \(i^3 = -i\), \(i^4 = 1\), and then the cycle repeats every 4 powers. So we can find the remainder when the exponent is divided by 4 to simplify \(i^{608}\).

Step2: Divide 608 by 4

Calculate \(608 \div 4\). Since \(4\times152 = 608\), the remainder is 0.

Step3: Determine \(i^{608}\)

When the remainder is 0 when dividing the exponent by 4, it means \(i^{608}\) is equivalent to \(i^4\) (because the cycle repeats every 4). And we know \(i^4 = 1\).

Answer:

\(1\)