Adding and Subtracting Complex Numbers Made Easy

The Organic Chemistry Tutor

This concise mathematics tutorial demonstrates the procedural steps for adding and subtracting complex numbers. The video guides viewers through three distinct examples of increasing complexity, starting with simple addition, moving to subtraction requiring distribution of a negative sign, and concluding with an expression involving scalar multiplication before combination. The instructor emphasizes the core strategy of treating real and imaginary components as separate "like terms" to be combined. Key themes include algebraic manipulation, the distributive property, and the standard form of complex numbers ($a + bi$). The video specifically highlights common student pitfalls, such as failing to distribute negative signs to both terms in a parenthesis, and demonstrates how to organize work to avoid calculation errors. The use of color-coding (red for real numbers, blue for imaginary numbers) helps visually distinguish between the components. For educators, this video serves as an excellent model for direct instruction or remediation in an Algebra II or Pre-Calculus curriculum. It effectively scaffolds learning by starting simple and adding procedural layers. Teachers can use this resource to reinforce the parallel between combining algebraic expressions with variables (like $3x + 2x$) and operating with imaginary numbers, helping students build upon prior knowledge to master new concepts.