Higher Powers of I: Recognizing Patterns

This lesson teaches how to evaluate higher powers of the imaginary unit i by recognizing patterns. It reviews mathematical rules such as the product and quotient rules, and the power of zero. The video explains how to evaluate powers of i, identify cycles and patterns, and apply these patterns to simplify higher powers. By understanding these patterns, students can easily determine the value of i raised to any power.

What is the value of i squared?

• -1

• 1

• -i

• i

How can i cubed be expressed in terms of i squared?

• i squared times i

• i squared plus i

• -i

• i

What is the value of i raised to the fourth power?

• -1

• i

• -i

• 1

What pattern do the powers of i follow?

• They are all negative

• They repeat every four powers

• They are all positive

• They increase linearly

If the exponent of i is a multiple of 4 plus 1, what is the result?

• -i

• -1

• i

• 1

How can you determine the value of i raised to a high power like 635?

• By adding 635 to the base

• By using the cyclical pattern and division

• By multiplying i 635 times

• By subtracting 635 from the base

What is the value of i raised to the 234th power?

• 1

• i

• -1

• -i