Simplify complex numbers

The video tutorial explains the concept of imaginary numbers, focusing on the imaginary unit 'i'. It describes how 'i' is defined as the square root of -1 and explores the powers of 'i', which follow a repeating pattern every four terms. The tutorial then demonstrates how to calculate 'i' to the 67th power by dividing 67 by 4 and using the remainder to determine the equivalent power of 'i'. The lesson concludes with encouragement for viewers to engage further with the material.

What is the value of 'i' squared?

• 1

• -1

• -i

• i

Which of the following represents the value of 'i' to the fourth power?

• -1

• -i

• 1

• i

How often does the pattern of powers of 'i' repeat?

• Every 5 terms

• Every 4 terms

• Every 3 terms

• Every 2 terms

What is the remainder when 67 is divided by 4?

• 0

• 3

• 2

• 1

What is the value of 'i' to the 67th power?

• 1

• -i

• -1

• i