Complex Numbers Course
Master complex numbers from the ground up — from standard form and the complex plane all the way to analytic functions, contour integration, and real-world applications in engineering and physics. This course builds rigorous understanding through clear theory, worked examples, and practical problem-solving. Whether you are a student, engineer, or mathematician, you will gain the tools to handle complex analysis with confidence.
from 4 to 360h flexible workload
valid certificate in your country
What will I learn?
This course covers every essential topic in complex number theory, starting with the definition of i and the structure of the complex plane. You will master arithmetic operations, modulus, argument, and polar form before advancing to De Moivre's theorem and nth roots. The course then moves into polynomial equations, complex functions, and the Cauchy-Riemann equations that define analytic functions. You will also explore contour integration, the residue theorem, and applications in electrical circuits, signal processing, and fluid dynamics. By the end, you will have a complete, rigorous foundation in complex analysis ready for advanced mathematics and engineering work.
Elevify advantages
Develop skills
- Polar and Exponential Form: Convert complex numbers fluently between rectangular, polar, and exponential representations.
- Complex Arithmetic: Add, subtract, multiply, and divide complex numbers accurately using standard procedures.
- Analytic Functions: Apply Cauchy-Riemann equations to test differentiability and identify analytic functions.
- Real-World Modelling: Use complex impedance, phasors, and Fourier methods to solve engineering problems.
Suggested summary
Before starting, you can change the chapters and the workload. Choose which chapter to start with. Add or remove chapters. Increase or decrease the course workload.What our students say
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