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 does the remainder of 1 indicate when simplifying I to the 77th power?

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How can I to the 77th power be rewritten based on the simplification process discussed?

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