Algebra 2 - How do you simplify a complex number to a high power i^ 31

The video tutorial explains the concept of the imaginary unit i, starting with its definition as the square root of -1. It covers the calculation of i squared, i cubed, and higher powers, highlighting the repeating pattern every four exponents. The tutorial introduces modular arithmetic as a method to simplify calculations of higher powers of i, using division to find remainders and determine the equivalent power. The video concludes with a discussion on shortcuts for calculating powers of i efficiently.

What does I to the 4th power equal and why is this important?

Describe the process of finding the exponent when it exceeds 4.

What is the significance of the remainder when dividing the exponent by 4?