### About Simplifying Powers of i:

In order to simplify powers of i, we must know the result for raising i to the first four powers and our rules of exponents. We should understand that i raised to the first power is simply i, i raised to the second power is -1, i raised the third power is -i, and i raised to the fourth power is 1. We can use these tools to simplify any power of i.

Test Objectives

- Demonstrate the ability to simplify a power of the imaginary unit i

#1:

Instructions: simplify each.

$$a)\hspace{.2em}i^{30}$$

$$b)\hspace{.2em}i^{52}$$

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#2:

Instructions: simplify each.

$$a)\hspace{.2em}i^{27}$$

$$b)\hspace{.2em}i^{201}$$

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#3:

Instructions: simplify each.

$$a)\hspace{.2em}i^{309}$$

$$b)\hspace{.2em}i^{-58}$$

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#4:

Instructions: simplify each.

$$a)\hspace{.2em}i^{-222}$$

$$b)\hspace{.2em}-i^{-101}$$

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#5:

Instructions: simplify each.

$$a)\hspace{.2em}-i^{-229}$$

$$b)\hspace{.2em}\frac{1}{-i^{-79}}$$

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}-1$$

$$b)\hspace{.2em}1$$

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#2:

Solutions:

$$a)\hspace{.2em}-i$$

$$b)\hspace{.2em}i$$

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#3:

Solutions:

$$a)\hspace{.2em}i$$

$$b)\hspace{.2em}-1$$

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#4:

Solutions:

$$a)\hspace{.2em}-1$$

$$b)\hspace{.2em}i$$

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#5:

Solutions:

$$a)\hspace{.2em}i$$

$$b)\hspace{.2em}i$$