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Back to Complex Analysis
Intermediate 10 Hours Article 20.1–20.5

Introduction to Complex Analysis

Complex numbers, limits, continuity, and analytic functions

✓ Live group sessions (full course duration) ✓ Dedicated doubt-clearing within the batch

Pricing (per student)

10+ students
₹175 / hr
Total: ₹1,750
15+ students
₹150 / hr
Total: ₹1,500
20+ students
₹125 / hr
Total: ₹1,250

Prerequisites

  • Basic calculus (differentiation, integration)
  • Familiarity with algebra and trigonometry

Overview

Introduces students to the fundamentals of complex numbers and functions, ensuring they understand limits, continuity, and differentiability in the complex plane. Builds the foundation needed for all subsequent Complex Analysis courses.

Topics

HourTopicDetails
1Introduction to Complex NumbersDefinition, representation, algebraic operations.
2Complex Plane & Polar FormArgand diagram, polar form, De Moivre's theorem.
3Functions of a Complex VariableDefinition, examples, domain, and range.
4Limits in Complex AnalysisDefinition, examples, and geometric interpretation.
5Continuity in the Complex PlaneDefinition, conditions, and examples.
6Differentiability of Complex FunctionsDefinition and Cauchy-Riemann conditions (Cartesian form).
7Analytic FunctionsDefinition, properties, and examples.
8Problems on Cauchy-Riemann EquationsSolving problems to verify analyticity.
9Construction of Analytic FunctionsIntroduction to the Milne-Thompson method.
10Recap & Problem-Solving SessionRevision, doubt clearance, and timed practice problems.

Expected Outcomes

  • Understand complex numbers and their geometric representation.
  • Solve problems on limits, continuity, and differentiability.
  • Apply Cauchy-Riemann equations to check analyticity.