This chapter provides a comprehensive review of complex numbers, serving as an essential foundation for engineering and scientific analysis. It begins by defining complex numbers as extensions of the real number system, introducing the imaginary unit and the standard rectangular form consisting of real and imaginary parts. The text explores the practical necessity of these numbers as roots of second-order polynomial equations where the discriminant is negative. Key concepts include the geometric representation of complex numbers on the complex plane, the calculation of magnitude, and the determination of the principal argument within the standard range. Special emphasis is placed on Euler’s formula, which facilitates the conversion between Cartesian and polar forms, alongside an exploration of complex conjugates and the complex exponential function. The chapter concludes with practical computational techniques using MATLAB, demonstrating how to perform basic arithmetic, trigonometric operations, and coordinate conversions to streamline complex mathematical problem-solving in fields like electrical engineering and fluid dynamics.