Complex Numbers: From First Principles to Advanced Problem Solving

Master the Imaginary with Geometric Intuition and Algebraic Rigor

Complex numbers are often taught as a mechanical set of rules to solve x2+1=0x2+1=0. In Complex Numbers: From First Principles to Advanced Problem Solving , Rishabh Kumar—an alumnus of IIT Guwahati and the Indian Statistical Institute (ISI) —redefines the subject as a powerful, unified language for rotation, symmetry, and structural beauty.

This book is more than a textbook; it is a structured roadmap that takes you from the absolute foundations to the frontiers of Olympiad and university-level mathematics. By emphasizing Visual Intuition First, it transforms abstract symbols into a vivid, two-dimensional reality.

Inside this Comprehensive Journey: The Foundation (Phase I): Master the algebraic core—from the cyclic nature of i to the intricacies of the triangle inequality.

Geometry & Representation (Phase II): Visualize the Argand plane through Cartesian, Polar, Vector, and Exponential forms.

Structural Mastery (Phase III): Unlock the full power of De Moivre’s Theorem, nth roots of unity, and the geometry of regular polygons.

Locus & Transformations (Phase IV): Conquer the most challenging topics—straight lines, circles, rotations, and Möbius transformations.

Advanced Applications (Phase V): Bridge the gap to higher math with inequalities, polynomials, and functional equations in the complex domain.

The Problem Universe (Phase VI): Challenge yourself with a tiered ecosystem of problems, including objective questions, comprehension sets, and Olympiad-level challenges (RMO, INMO, IMO).

Why This Book is Different: Elite Credentials: Written by a mentor with a strong academic background with over 7 years of teaching experience.

The Why Before the How: Every concept is developed through structural reasoning, ensuring you never have to rely on rote memorization again.

Targeted for Excellence: Specifically designed for students aiming for the JEE Advanced, ISI / CMI Entrance, and National / International Math Olympiads.

Comprehensive Appendices: Includes specialized sections on Coordinate Geometry and Trigonometry via complex numbers.

About the Author : Rishabh Kumar is a mathematician, author, and founder of Mathematics Elevate Academy . His teaching philosophy—centered on clarity, depth, and the pursuit of elegant solutions—has helped thousands of students achieve excellence in the world’s toughest competitive examinations.

Stop viewing complex numbers as complex. Start seeing them as a tool for mathematical mastery. Scroll up and begin your journey today!