(1.4 hours to learn)
Complex numbers are numbers expressible as a + bi, where i^2 = -1. They are often more convenient to work with than real numbers, because all complex (and hence all real) polynomials of degree n have n complex roots. Many trigonometric identities can be derived more simply using complex numbers.
-this concept has no prerequisites-
- Be able to add, multiply, and divide complex numbers, and raise them to powers
- Know the definitions of
- complex conjugate
- norm (or absolute value) of a complex number
- Why can't i and -i be distinguished?
- Be able to work with the polar representation of complex numbers
Core resources (read/watch one of the following)
→ Khan Academy: Algebra
→ The Road to Reality (2007)
An overview of much of mathematical physics.
Location: Chapter 4, "Magical complex numbers"
Supplemental resources (the following are optional, but you may find them useful)
→ Introduction to Linear Algebra
An introductory linear algebra textbook with an emphasis on numerical methods.
Location: Section 10.1, "Complex numbers," pages 493-498
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