Then we looked at the pattern with the powers of i by creating a circle (used the clock analogy) and rewriting the power with i, i^2, i^3, or i^4. We saw that we could rewrite this different ways and still have the same value. Students were able to look at the exponent (of i) and determine if it was a multiple of 4, then it had a value of 1. We stressed finding the correct placement on the circle for the even power and then moving forward or backwards from there.
Use the video links for review or practice on the power of i
https://www.youtube.com/watch?v=KhdZvfH6fGg
https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-imaginary-numbers-algebra-2/v/calculating-i-raised-to-arbitrary-exponents
How did we get imaginary numbers?
https://www.youtube.com/watch?v=T647CGsuOVU
https://www.youtube.com/watch?v=2HrSG0fdxLY
https://www.youtube.com/watch?v=N9QOLrfcKNc
https://www.youtube.com/watch?v=DThAoT3q2V4
https://www.youtube.com/watch?v=65wYmy8Pf-Y
https://www.youtube.com/watch?v=z5IG_6_zPDo
https://www.youtube.com/watch?v=YHvR8siIiD0
HW: Complete the Powers of i Worksheet (both sides)