MASTER Simplifying a imaginary number to a higher power

The video tutorial explains how to simplify complex numbers raised to higher powers by focusing on the imaginary unit I. It covers the basic properties of I, including its powers, and identifies a repeating pattern every four powers. The tutorial demonstrates how to simplify higher powers of I by dividing the exponent by four and using the remainder to determine the equivalent power of I. Several examples are provided to illustrate the process.

What is the significance of every fourth power of I in the context of complex numbers?

How do you determine the equivalent power of I when given a large exponent, such as I to the 120th?

What is the result of I to the 40th power and how is it derived?