Intro to COMPLEX NUMBERS // Motivation, Algebraic Definition & Fundamental Theorem of Algebra Ep. 1

Welcome to my new series, an Introduction to Complex Numbers. In this Part 1 I give an introduction to the algebraic story. One of the main motivations for studying Complex and Imaginary numbers is just to solve equations like x^2=-1, and much like we defined the number root 2 to be a solution to x^2=2, similarly we define i= sqrt(-1) as the positive solution to x^2=-1. We then develop a precise definition, defining the addition and multiplication of complex numbers. We finish by discussing the Fundamental Theorem of Algebra which states that any nth degree polynomial has exactly n complex solutions when counted with multiplicity, a beautiful result that makes our lives much easier when working with complex numbers than just with real numbers. Episode 2 of this series focusing on the geometry of complex number will be posted next week in the Calculus II playlist below: COURSE PLAYLISTS: ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►DIFFERENTIAL EQUATIONS (Calc IV):    • How to solve ODEs with infinite series | I...   ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   OTHER PLAYLISTS: ► Want to learn math effectively? Check out my "Learning Math" Series:    • 5 Tips To Make Math Practice Problems Actu...   ►Want some cool math? Check out my "Cool Math" Series:    • Cool Math Series   BECOME A MEMBER ►Join:    / @drtrefor   MATH BOOKS I LOVE (affiliate links): Infinite Powers: https://www.amazon.com/gp/product/132... Math with Bad Drawings: https://www.amazon.com/gp/product/031... Godel, Escher, Bach: https://www.amazon.com/gp/product/046... Teach Yourself How to Learn: https://www.amazon.com/gp/product/162... Proofs from THE BOOK: https://www.amazon.com/gp/product/366... The Man who Knew Infinity https://www.amazon.com/gp/product/147... SOCIALS: ►Twitter (math based):   / treforbazett   ►Instagram (photography based):   / treforphotography