Question

What is the value of \( i^{4k+2} \) where \( k \) is an integer?

• A. \(1 \)
• B. \(-1 \)
• C. \(i \)
• D. \(-i \)

Hint:

Memorize the power cycle of \(i\): \(i,-1,-i,1\). The pattern repeats every 4 powers, making higher powers easy to simplify.

Answer 1

The Correct Option is B

Concept: Powers of i repeat every four: i¹=i, i²=–1, i³=–i, i⁴=1. For any integer k, i⁴ᵏ = 1.

Step 1: Decompose the exponent.
i^(4k+2) = i⁴ᵏ × i² = 1 × (–1) = –1.

Final Answer: –1 (option B).