Algebra 2 - Evaluating complex numbers to a higher power i^ 65

The video tutorial explains the cyclical nature of powers of the imaginary unit 'i'. It demonstrates how powers of 'i' repeat every four exponents, and how to calculate the remainder when dividing exponents by four to determine the equivalent power of 'i'. The tutorial emphasizes that the remainder is crucial in identifying the power of 'i' after repetitions. The explanation includes examples and calculations to illustrate these concepts, ensuring a clear understanding of the cyclical pattern and its implications.

What is the result of i squared?

• 1

• -1

• -i

• i

What happens to the powers of 'i' after every fourth power?

• They become zero

• They repeat

• They double

• They become negative

If you have i to the 5th power, what is it equivalent to?

• i

• 1

• -i

• -1

When dividing the exponent of 'i' by 4, what is the significance of the remainder?

• It tells you how many times it repeats

• It determines the equivalent power of 'i'

• It shows the negative power

• It is not important

What does a remainder of 0 indicate when dividing the exponent of 'i' by 4?

• The power is -1

• The power is zero

• The power is one

• The power is i