Simplify complex numbers

The video tutorial explains how to simplify imaginary numbers, focusing on the properties and powers of the imaginary unit 'i'. It covers the cyclical nature of i's powers, showing that every fourth power returns to 1. The tutorial provides a method to simplify higher powers of i by dividing the exponent by 4 and using the remainder to determine the result. This approach is applied to solve problems involving powers of i, emphasizing the repeating cycle and simplification techniques.

What is the value of 'i' squared?

• i

• -1

• 0

• 1

Which power of 'i' results in the value of 1?

• i^2

• i^3

• i^4

• i^5

What happens to the powers of 'i' after every four cycles?

• They become zero

• They double

• They reset to 1

• They become negative

How do you determine the value of i^25?

• Multiply 25 by 4

• Divide 25 by 4 and use the remainder

• Subtract 4 from 25

• Divide 25 by 4 and use the quotient

If the remainder is 3 when dividing the exponent by 4, what is the value of 'i' raised to that power?

• i

• -1

• -i

• 1