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Introduction to Complex and Imaginary Numbers for General Studies

The free online course teaches you about complex and imaginary numbers, as well as transformations of functions.

If you are a professional, a student or someone with a keen interest in understanding complex numbers and types of functions, this course has been designed especially to help you. Study the characteristics of functions and function notation before focusing on the different types of special functions. The material covers arithmetic operations, composition, and the graphical and multiple transformations of a function.

4-5 Hours

82

CPD

Description

Complex and imaginary numbers 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’s 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, rationalizing 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, the rules of the piece-wise defined and signum functions.

How to perform various arithmetic operations composition and 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 the 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.

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