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