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.Publisher: ADU
CertificationView course modules
Complex and imaginary numbers is a free online course that has been specifically prepared to teach you about pure imaginary numbers. When working with imaginary numbers, you should take time to learn about the addition, subtraction and other operation 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 important. To perform algebraic operations with the imaginary number i, it’s necessary to know 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. It is also important that you learn about the algebraic rules for the multiplication of two binomials, multiple ways to represent a function, along with the behavior and characteristics of functions.
If you want to learn about the different types of special functions, as well as their properties, then you should complete this course. You will also be able to identify the different special functions from their equations and how to plot their graphs. The differences between the constant and identity functions will be covered in this course. This course can also help you understand the algebraic definitions of the absolute value functions. You will also be able to learn about the properties of the linear and greatest integer function. Do you know that when the graph of a quadratic function is plotted, the resulting figure is called a parabola? To have a better understanding about 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 in this course. You will also learn about the differences, domain, properties along with the rules of the piece-wise defined and signum functions.
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Furthermore, you can also learn about how to perform different arithmetic operations composition and inverse of a function. Do you know that a graph may be translated vertically, horizontally or both? To gain more insight on this, you will need to understand the concepts and properties of translations. You will learn about the graphical transformations of functions. You will also learn about dilations and reflections over the x, as well as the y-axis. This course will also help you get familiar with the properties preserved under a point reflection. You will be able to understand the multiple transformations of a function, and the order in which transformations are performed upon a prototype. You will also be familiar with finding the inverse of functions and proving how functions are inverses. This free online course will be of great interest to students, researchers, and anyone with an interest in understanding the complex and imaginary numbers. So, register for this course and start your next learning journey today.
Imaginary Numbers and Functions
Imaginary Numbers and Functions - Learning Outcomes
Basic Operations and Conjugates of Complex Numbers
Relations and Functions
Imaginary Numbers and Functions - Lesson Summary
Graphical Transformations of Functions
Graphical Transformations of Functions - Learning Outcomes
Other Special Functions
Arithmetic Operations on Functions
Translations, Reflections and Dilations
Graphical Transformations of Functions - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Discuss the concepts of imaginary numbers.
- Explain the imaginary unit, denoted "i".
- Discuss the field of complex numbers.
- Outline how to perform operations on imaginary numbers and on complex numbers.
- Describe the concepts of functions.
- State the meaning of domain and range of a function.
- Identify the domain and range of the different special functions and how to draw their graphs.
- State how to perform arithmetic operations on functions.
- Discuss the composition of functions and how to form the composite of two or more functions.
- Explain the inverse of a function.
- Outline how a function can be analyzed as a modification of a basic prototype.
- State how to transform geometric figures through translations, reflections, rotations and dilations.
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