What is i^3?

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Prepare for the A Level Further Mathematics Core Pure Test with detailed explanations and challenging questions. Boost your understanding and confidence to excel in your exam!

Multiple Choice

What is i^3?

Explanation:
Powers of i form a four-step cycle because i^2 = -1. Each extra multiplication by i moves one step along: i^3 = i^2 × i = (-1) × i = -i. You can also see the repeating sequence i, -1, -i, 1, then back to i. So the third power gives -i, not i, -1, or 1.

Powers of i form a four-step cycle because i^2 = -1. Each extra multiplication by i moves one step along: i^3 = i^2 × i = (-1) × i = -i. You can also see the repeating sequence i, -1, -i, 1, then back to i. So the third power gives -i, not i, -1, or 1.

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