- Be able to perform basic arithmetic operations with complex numbers.
- Understand the different forms used to express complex numbers (cartesian, polar and complex exponentials).
- Calculate the complex conjugate and the modulus of a number expressed in the different forms (cartesian, polar and complex exponentials).
- Be able to manipulate complex functions.
- Be able to obtain expressions for the complex conjugate and the square of the modulus of a complex function.
- 2.1: Algebra with Complex Numbers
- The imaginary unit i is defined as the square root of -1.
- 2.2: Graphical Representation and Euler Relationship
- Complex numbers can be represented graphically as a point in a coordinate plane. In cartesian coordinates, the x -axis is used for the real part of the number, and the y -axis is used for the imaginary component. Complex numbers can be also represented in polar form. We can also represent complex numbers in terms of complex exponentials.
- 2.3: Complex Functions
- The concepts of complex conjugate and modulus that we discussed above can also be applied to complex functions.
Thumbnail: A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and i satisfies \(i^2 = −1\). (CC BY-SA 3.0 unported; Wolfkeeper via Wikipedia)