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
Simplifying Powers of i Practice Test:

#1:

Instructions: simplify each.

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

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


#2:

Instructions: simplify each.

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

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


#3:

Instructions: simplify each.

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

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


#4:

Instructions: simplify each.

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

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


#5:

Instructions: simplify each.

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

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


Written Solutions:

#1:

Solutions:

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

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


#2:

Solutions:

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

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


#3:

Solutions:

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

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


#4:

Solutions:

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

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


#5:

Solutions:

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

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