Pre-Calculus - How to simplify imaginary numbers to a higher power

The video tutorial introduces the concept of imaginary numbers, focusing on the imaginary unit 'i' and its properties. It explains how to calculate higher powers of 'i' and identifies a repeating pattern every four powers. The tutorial demonstrates how to use divisibility and remainders to simplify calculations involving powers of 'i'. The session concludes with practical applications, encouraging students to apply these concepts to solve mathematical problems.

What is the imaginary unit 'i' defined as?

• The cube root of a positive number

• The square root of a negative number

• The square root of a positive number

• The cube root of a negative number

What is the value of i squared?

• -i

• i

• -1

• 1

What is the value of i to the fourth power?

• i

• -i

• 1

• -1

What is the value of i to the sixth power?

• -1

• -i

• i

• 1

If i to the 8th power equals 1, what is i to the 12th power?

• -1

• 1

• -i

• i

How do you determine the value of i to the 17th power?

• By dividing 17 by 3

• By dividing 17 by 4 and using the remainder

• By multiplying 17 by 4

• By subtracting 4 from 17

What is the equivalent power of i to the 83rd power?

• -1

• 1

• -i

• i