Tutorial - Rewriting an imaginary number when it is raised to a higher power ex 5, i^10

The video tutorial explains how to simplify imaginary numbers raised to higher powers, specifically focusing on i to the 10th power. It introduces the cyclical nature of powers of i, where i to the 4th equals 1, and demonstrates how to use the power rule of exponents to simplify expressions. By breaking down i to the 10th into components of i to the 4th and i squared, the tutorial shows that i to the 10th simplifies to -1.

What happens to the powers of 'i' when you reach the fifth power?

• They continue to increase linearly.

• They reset to the first power.

• They become undefined.

• They double in value.

Which rule allows you to add the exponents when multiplying like bases?

• Associative Rule

• Power Rule of Exponents

• Distributive Rule

• Commutative Rule

How can 'i' to the 10th power be expressed using 'i' to the 4th power?

• As a sum of 'i' to the 4th power and 'i' to the 6th power

• As a difference of 'i' to the 4th power and 'i' squared

• As a product of 'i' to the 4th power and 'i' to the 6th power

• As a product of two 'i' to the 4th powers and 'i' squared

What is the value of 'i' to the 4th power?

• i

• -1

• 1

• 0

What is the final simplified value of 'i' to the 10th power?

• 0

• i

• -1

• 1