This is a captivating course that has been specifically developed to teach you about pure imaginary numbers. When working with imaginary numbers, you should learn about the addition, subtraction and other operations of imaginary numbers. This course also analyzes the concepts of the field of complex numbers. If you are asked about combining pure imaginary numbers with real numbers, you should know that the field of complex numbers is essential to do this. For example, to perform algebraic operations with the imaginary number ‘i’, it is necessary to understand how to raise ‘i’ to any power. Do you know that a complex plane consists of a real number line and a number line for all the pure imaginary numbers? Prepare yourself to learn about the conjugates and division of a complex number, rationalising denominators, domain and range of a relation as well as the vertical and horizontal line test for a function. Likewise, you must learn about the algebraic rules for the multiplication of two binomials, multiple ways to represent a function and behaviour and characteristics of functions.
If you want to learn about the different types of special functions and their properties, you should complete this course. You will be able to identify the other special functions from their equations and plot their graphs. We will cover the differences between the constant and identity functions, help you understand the algebraic definitions of the absolute value functions and teach you the linear and greatest integer function properties. Do you know that when you plot the graph of a quadratic function, the resulting figure is called a ‘parabola’? To better understand the parabola, you will also need to understand the vertex and its coordinates. It is also imperative that you learn about the features and differences between polynomial and rational functions. The equation and graph of an exponential function will also be covered extensively, along with the differences, domain, properties and the rules of the piecewise and signum functions.
Learning how to perform various arithmetic operations and calculate the inverse of a function will challenge your thinking and round off the course. For example, do you know that a graph may be translated vertically, horizontally or both? Gain insight by understanding the concepts and properties of ‘translations’. Learn about the graphical transformations of functions and dilations, and reflections over the x- and y-axis. We will help you become familiar with the properties preserved under a point reflection and assist you in understanding the multiple transformations of a function and the order in which they are performed upon a prototype. Finally, we will guide you with finding the inverse of functions and proving how functions are inverses. Students, researchers and anyone interested in understanding complex and imaginary numbers will find this course worthwhile. So register today.
