The Imaginary Unit i and Its Powers (Algebra 2)

Free printable Algebra 2 algebra worksheet on the imaginary unit i, simplifying powers of i through the i, -1, -i, 1 cycle, and writing square roots of negative numbers in terms of i.

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Algebra 2 · Math worksheet

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Algebra 2: The Imaginary Unit i and Its Powers

Simplify each power of i using the cycle i, i² = -1, i³ = -i, i⁴ = 1, and write each square root of a negative number in terms of i.

1.
Simplify: $i^{40}$
2.
Simplify: $i^{29}$
3.
Simplify: $i^{2}$
4.
Simplify: $i^{5}$
5.
Simplify: $i^{6}$
6.
Simplify: $i^{8}$
7.
Simplify: $\sqrt{-12}$
8.
Simplify: $\sqrt{-525}$
9.
Simplify: $\sqrt{-931}$
10.
Simplify: $\sqrt{-32}$
11.
Simplify: $\sqrt{-224}$
12.
Simplify: $\sqrt{-5}$

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