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 II: ►MULTIVARIABLE CALCULUS (Calc III): ►DIFFERENTIAL EQUATIONS (Calc IV): ►DISCRETE MATH: ►LINEAR ALGEBRA: OTHER PLAYLISTS: ► Want to learn math effectively? Check out my "Learning Math" Series: ►Want some cool math? Check out my "Cool Math" Series: BECOME A MEMBER ►Join: MATH BOOKS I LOVE (affiliate links): Infinite Powers: =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=1328879984&linkId=e25e50aa88007ff0efef1054e3abdc16 Math with Bad Drawings: =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=0316509035&linkId=6a70ac5233c6f629efdede2e5b0c110c Godel, Escher, Bach: =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=0465026567&linkId=3a88808f24c4d5debd705ab443a81faa Teach Yourself How to Learn: =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=1620367564&linkId=29071012794b2fbe923a10f163fe0502 Proofs from THE BOOK: =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=3662572648&linkId=82699c064093fb6dca2e133917ee088a The Man who Knew Infinity =as_li_tl?ie=UTF8&tag=trefor-20&camp=1789&creative=9325&linkCode=as2&creativeASIN=1476763496&linkId=f3a354869108be3ee5931e0ad0812932 SOCIALS: ►Twitter (math based): ►Instagram (photography based):