Rewrite i simplified when it is raised to a higher power

The video tutorial explains how to simplify expressions involving powers of the imaginary unit i. It begins by reviewing the cyclical nature of i's powers: i, -1, -i, and 1. The tutorial then demonstrates how to determine the remainder when dividing the exponent by 4, which helps in simplifying the expression. By applying this method, the video shows that i to the 77th power simplifies to 7i.

What is the value of i squared?

• -i

• i

• -1

• 1

How often do the powers of i repeat?

• Every 2 powers

• Every 3 powers

• Every 4 powers

• Every 5 powers

What is the remainder when 77 is divided by 4?

• 2

• 1

• 0

• 3

If i to the 77th power is simplified, what is the result?

• -i

• 1

• -1

• i

What is the simplified form of 7 times i to the 77th power?

• -7i

• -7

• 7i

• 7