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Best resources to learnComplex Numbers

Study sheet

Complex numbers extend the real number system by introducing the imaginary unit. Learners will understand algebraic operations, polar representation, Euler's formula, and how to solve polynomial equations that have no real roots.

Where to start

Start with Introduction to Complex Analysis, a free Coursera course from Wesleyan University taught by Petra Bonfert-Taylor, which covers complex numbers before analytic functions and contour integration. If you only use one resource, make it Visual Complex Analysis by Tristan Needham, a visual treatment of the subject. For the full theory, continue with Complex Variables with Applications (MIT 18.04) by Jeremy Orloff.

6 resources · · How we curate

🎓Courses(3)

course

Complex Analysis

Dive into complex numbers with Dr. Bazett's Complex Analysis course! Learn essential theory and problem-solving techniques.

advanced🇬🇧
course

Complex Variables with Applications (MIT 18.04)

Complex analytic functions and their applications: Cauchy's theorem and integral formula, Taylor and Laurent series, residues for evaluating hard integrals, harmonic functions, conformal maps, two-dimensional fluid flow, and Laplace and Fourier transforms. Provides 14 lecture note files plus problem sets and exams with solutions.

intermediate🇬🇧
course

Introduction to Complex Analysis

Wesleyan University course on complex analysis covering complex numbers, analytic functions, conformal mappings, Möbius transformations, contour integration, Cauchy's theorem, power and Laurent series, and residues. Learners finish able to evaluate contour integrals and analyze complex-differentiable functions.

intermediate🇬🇧

📚Books(2)

bookPaid

Complex Variables and Applications

Standard undergraduate textbook on complex variables for mathematics, physics and engineering students. Covers analytic functions, elementary functions, contour integrals, Cauchy's theorem, Taylor and Laurent series, residues and conformal mapping, teaching readers to evaluate real integrals and solve boundary-value problems.

intermediate🇬🇧
bookPaid

Visual Complex Analysis

Geometric introduction to complex analysis that explains results through pictures rather than heavy computation. Covers Möbius transformations, the complex derivative as an amplitwist, non-Euclidean geometry, winding numbers, Cauchy's theorem and vector fields, building intuition for why the standard theorems are true.

intermediate🇬🇧

🌐Websites(1)

website

Wolfram MathWorld

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

intermediate🇬🇧
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Frequently Asked Questions

Where should I start learning Complex Numbers?

Start with Introduction to Complex Analysis, a free Coursera course from Wesleyan University taught by Petra Bonfert-Taylor, which covers complex numbers before analytic functions and contour integration. If you only use one resource, make it Visual Complex Analysis by Tristan Needham, a visual treatment of the subject. For the full theory, continue with Complex Variables with Applications (MIT 18.04) by Jeremy Orloff.

What are the best free resources to learn Complex Numbers?

Dantes has curated 6 resources for Complex Numbers, including 2 books, 3 courses, 1 websites. All resources are hand-picked for quality — no algorithmic filler. Browse the full list above to find the format that works best for you.

Is Complex Numbers hard to learn?

Complex Numbers is approachable at the beginner level — there are resources here specifically for those starting from scratch. As you progress, intermediate and advanced material is also available to take your skills further.

What types of Complex Numbers learning resources are available on Dantes?

For Complex Numbers, Dantes has curated 2 books, 3 courses, 1 websites. Each resource type serves a different learning style: videos and YouTube for visual learners, books for depth, courses for structured progression, and websites for quick reference.

How does Dantes select Complex Numbers resources?

Dantes is an algorithm-free learning directory. Resources are hand-curated based on quality, accuracy, and usefulness — not engagement metrics or paid placements. The goal is to surface the best learning material for Complex Numbers, whether it's a free YouTube series, a classic textbook, or an open courseware from a top university.

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