This course on complex numbers aims to provide a comprehensive understanding of the basics of complex numbers and their applications. By the end of the course, learners will be able to represent complex numbers in Cartesian and polar forms, understand Euler's formula and identity, perform various operations on complex numbers, and apply de Moivre's theorem to find nth roots. The teaching method involves a series of video lectures covering different topics with detailed explanations and proofs. This course is intended for individuals interested in mathematics, particularly those looking to strengthen their knowledge of complex numbers and complex analysis.
Overview
Syllabus
Sarcastic and serious introductions.
1.1 Complex plane - Cartesian way.
1.2 Complex plane - Polar way (Intro).
1.3 Arguments about arguments.
1.4 Interconversion .
2.1 Euler's formula - classic proof.
2.2 Euler's formula - 2nd proof.
3.1 Operations - addition/subtraction.
3.2 Operations - multiplication.
3.3 Operations - conjugation.
3.4 Operations - division.
3.5 Operations - exponentiation.
3.6 Operations - logarithm.
3.7 Operations - sine/cosine.
4.1 de Moivre's theorem - intro.
4.2 de Moivre's theorem - nth roots.
4.3 de Moivre's theorem - Euler's formula 3rd proof.
Outro.
Taught by
Mathemaniac
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