Simplifying Powers of the Imaginary Unit i

The Organic Chemistry Tutor

A clear, step-by-step mathematics tutorial focusing on simplifying integer powers of the imaginary unit 'i'. The video begins by defining the fundamental cyclical pattern of 'i' ($i$, $-1$, $-i$, $1$) and explains the logic behind why these values repeat every four powers. The instructor emphasizes memorizing these base values as the foundation for solving more complex problems. The core of the video demonstrates a reliable technique for simplifying high exponents by decomposing them into a multiple of 4 and a remainder. The instructor walks through several examples of increasing difficulty, starting with single-digit exponents like $i^7$, moving to larger numbers like $i^{189}$, and concluding with a binomial expression involving multiple terms. A specific calculator strategy involving decimals is also introduced to help identify remainders quickly. This resource is highly valuable for Algebra 2 and Pre-Calculus classrooms as a direct instructional tool or review aid. It effectively scaffolds the learning process, moving from conceptual understanding to procedural fluency. Teachers can use this video to support lessons on complex numbers, specifically helping students grasp how to manipulate exponents within the complex number system.