Complex Numbers: The Complete Masterclass | Full Course | Complete Series

Complex Numbers: The Complete Masterclass | Full Course | Complete Series Master every aspect of Complex Numbers in this comprehensive "Complete Series" masterclass. Whether you are preparing for Further Maths exams or university-level Engineering, this step-by-step guide covers everything from basic arithmetic to advanced transformations and loci. In this video, I have compiled my entire Complex Numbers library into one seamless tutorial. We start with the basics of i and move through vector representations, De Moivre’s Theorem, and the geometric properties of Loci, finishing with four full exam-style question walkthroughs. CHAPTERS: 0:00 Introduction 1:26 Introduction to Complex Numbers 7:25 How to Add, Subtract, Multiply, and Divide Complex Numbers 22:29 Complex Numbers as Vector Addition 26:36 Complex Numbers as Vector Subtraction 29:40 The Modulus and Argument of a Complex Number 38:03 Relationship Between Moduli and Arguments in Products 40:47 Relationship Between Moduli and Arguments in Products 44:39 Complex Numbers in Exponential Form 50:18 Complex Numbers in Polar Form 57:41 De Moivre’s Theorem - Powers of Complex Numbers 1:06:16 Finding the nth Roots of Complex Numbers 1:13:34 Loci: Perpendicular Bisectors 1:18:03 Loci: Circles 1:22:31 Loci: Half-Lines 1:28:41 Exam Question 1 1:33:38 Exam Question 2 1:40:00 Exam Question 3 1:43:38 Exam Question 4 Key Learning Outcomes: Master z = x + iy arithmetic and the conjugate pair. Visualise complex numbers as vectors for addition and subtraction. Convert between Cartesian, Polar, and Exponential forms (reꜞᶿ ). Apply De Moivre’s Theorem to find powers and roots. Sketch complex loci including circles, perpendicular bisectors, and half-lines. Solve high-level exam questions with confidence. About JohnsMathsBook: I provide simple, clear explanations for complex mathematical topics. My goal is to help students of all ages overcome their struggles with math and achieve their academic goals.