Powers and Properties of i

This video tutorial explains how to simplify positive integer powers of i by examining the remainder when the exponent is divided by four. It begins with a review of the definition and properties of i, including i squared. The tutorial then explores patterns in both even and odd powers of i, highlighting a cyclical pattern that repeats every four powers. The video also provides a method for finding large powers of i by using long division to determine the remainder, which indicates the position in the cycle. This approach simplifies the process of calculating powers of i efficiently.

What is the value of i squared?

• i

• -1

• 1

• 0

Which of the following is true about i to the fourth power?

• It equals -i

• It equals -1

• It equals 1

• It equals i

What is the result of i to the sixth power?

• -i

• i

• -1

• 1

What pattern do odd powers of i follow?

• i, -i, i, -i

• i, -1, i, -1

• 1, -1, 1, -1

• -i, i, -i, i

What is the value of i to the fifth power?

• 1

• -1

• -i

• i

How many distinct values are there in the cycle of powers of i?

• 2

• 5

• 3

• 4

What is the value of i to the 20th power?

• -i

• i

• 1

• -1

If the exponent is a multiple of 4, what is the value of i raised to that power?

• 1

• -1

• -i

• i

What is the remainder when 75 is divided by 4?

• 0

• 3

• 1

• 2

What is the value of i to the 75th power?

• -1

• i

• -i

• 1