ACT Preparation / Unit 7 ACT 0615 short lesson, about 20 seconds
The Imaginary Unit and Its Powers
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The idea
The imaginary unit i satisfies i² = −1, so √−n = i√n for positive n. Powers of i cycle every four: i, −1, −i, 1.
In practice
√−36 = 6i. Since 10 = 4 · 2 + 2, i¹⁰ = i² = −1.
Where people slip
√−4 · √−9 is 2i · 3i, which is −6, not √36. Convert to i before multiplying.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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