How to reduce i to when given as a higher power

The video tutorial explains how to simplify complex numbers raised to higher powers by identifying repeating patterns in their exponents. It demonstrates how to rewrite exponents using known power properties, specifically focusing on powers of four, which simplify to one. The tutorial concludes by simplifying the expression to find the final answer, showing that I to the 7th can be rewritten as I to the third or negative I.

Explain the process of finding the remainder when simplifying the complex number.

What does I to the fourth power equal, and how does it relate to I to the third power?