IITJEE Mains • Mathematics New Syllabus
Module 02: Complex Numbers & Quadratics Hub
Master the domain of imaginary numbers and polynomial roots. Explore complex algebra, Argand planes, polar forms, and the deep mechanics of quadratic equations.
Topic 1.1 • Complex Basics
Algebra of Complex Numbers, Real/Imaginary Parts, and Equality
Topic 1.2 • Absolute Values
Properties of Modulus, Conjugate, and Triangle Inequalities
Topic 2.1 • Geometry of Z
Argand Diagram, Principal Argument, and Polar Representation
Topic 2.2 • Advanced Forms
Euler’s Formula, De Moivre’s Theorem, and their Applications
Topic 3.1 • Roots of Unity
Cube Roots of Unity (1, ω, ω²), nth Roots of Unity, and Properties
Topic 3.2 • Equations
Quadratic Equations in Real and Complex Number Systems, Nature of Roots
Topic 4.1 • Vieta’s Relations
Relation between Roots and Coefficients, and Formation of Equations
Topic 4.2 • Advanced Quadratics