Understanding Powers of i

The video tutorial explores the cyclical nature of powers of the imaginary unit i, demonstrating how to calculate high powers of i using this cyclical pattern. It covers examples like i to the 100th, 501st, 7,321st, 99th, and 38th powers, showing how to simplify these calculations by recognizing multiples of 4 and using exponent properties.

What is the cyclical pattern of the powers of i?

• i, -i, 1, -1

• 1, i, -1, -i

• -i, 1, -1, i

• 1, -1, i, -i

What is the value of i to the 100th power?

• i

• 1

• -i

• -1

How can you express i to the 501st power?

• i to the 500th power plus i to the 1st power

• i to the 500th power minus i to the 1st power

• i to the 500th power times i to the 1st power

• i to the 500th power divided by i to the 1st power

What is the value of i to the 501st power?

• i

• -i

• -1

• 1

What is the general form for i to any multiple of 4?

• i to the 4k + 2

• i to the 4k + 1

• i to the 4k + 3

• i to the 4k

What is the value of i to the 7,321st power?

• i

• -1

• -i

• 1

What is the highest multiple of 4 less than 99?

• 98

• 97

• 96

• 95

What is the value of i to the 99th power?

• -1

• 1

• -i

• i

How can you express i to the 38th power?

• i to the 36th power minus i squared

• i to the 36th power times i squared

• i to the 36th power divided by i squared

• i to the 36th power plus i squared

What is the value of i to the 38th power?

• 1

• -i

• -1

• i