Dividing Complex Numbers and Rationalizing the Denominator

The Organic Chemistry Tutor

This educational video provides a comprehensive tutorial on dividing complex numbers and simplifying expressions to standard form ($a + bi$). The instructor demonstrates the process of rationalizing the denominator, moving from simple monomial denominators to more complex binomial denominators. The video uses a step-by-step approach, showing how to eliminate imaginary units from the denominator by multiplying by $i$ or by using the complex conjugate. The content covers key mathematical themes including complex number arithmetic, the properties of the imaginary unit $i$ (specifically that $i^2 = -1$), and algebraic expansion using the FOIL method. The video progresses in difficulty, starting with basic examples like $3/5i$ and advancing to problems involving radicals and binomials such as $(4-2i)/(3+5i)$. Special attention is given to writing the final answer in the correct real and imaginary component format. For educators, this video serves as an excellent instructional resource for Algebra II or Pre-Calculus units on the complex number system. It is particularly useful for visual learners who benefit from watching algebraic steps written out in real-time. Teachers can use this video to introduce the concept of the complex conjugate, reinforce the mechanics of polynomial multiplication, or provide targeted remediation for students struggling with rationalizing denominators.