Complex Numbers: Introduction and Operations

This lecture introduces complex numbers, which were first introduced in the 16th century to express roots of equations with negative square roots. The lecture covers the notation of complex numbers, addition, multiplication, conjugates, Euler's formula, and trigonometric relationships. The instructor explains the concept of complex numbers in the context of general physics and mechanics, focusing on their applications in engineering. The lecture also includes a review of mathematical concepts such as derivatives. Through examples and illustrations, students learn how to manipulate complex numbers and apply them in various mathematical and physical contexts.