Exploring Powers of Imaginary Numbers

This lesson explores the powers of imaginary numbers, focusing on the properties of the imaginary unit 'i'. The video explains how to break down powers of 'i' into smaller components and identifies cyclic patterns that simplify calculations. By dividing powers by four, students can determine the equivalent power of 'i'. The lesson includes examples and encourages students to practice these concepts.

What is the value of i squared?

• -i

• 1

• i

• -1

How can i to the third power be expressed?

• i squared times i

• i to the fourth times i

• i squared times i squared

• i to the fifth times i

What is the value of i to the fourth power?

• -1

• 1

• -i

• i

What pattern do the powers of i follow?

• Exponential

• Random

• Linear

• Cyclic

How can you simplify i to the 37th power?

• i to the 37th is equivalent to 1

• i to the 37th is equivalent to -i

• i to the 37th is equivalent to -1

• i to the 37th is equivalent to i

What is the value of i to the 44th power?

• -1

• 1

• -i

• i

How can you express i to the 39th power?

• i to the 39th is equivalent to 1

• i to the 39th is equivalent to -1

• i to the 39th is equivalent to -i

• i to the 39th is equivalent to i

What is the value of i to the 102nd power?

• 1

• -i

• -1

• i

What is i to the 27th power equivalent to?

• -1

• i

• -i

• 1

What is i to the 16th power equivalent to?

• i

• 1

• -1

• -i