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Available courses

COMPLEX NUMBERS

Welcome to Complex Numbers. This course introduces one of the most important extensions of the number system in mathematics. Complex numbers allow us to solve equations that have no real-number solutions and provide powerful tools used in engineering, physics, computer science, economics, and advanced mathematics.

Throughout this course, you will develop a solid understanding of complex numbers, learn how to perform operations with them, and explore their geometric and practical applications.

Course Objectives

By the end of this course, learners should be able to:

1.Define and interpret complex numbers.

2. Identify the real and imaginary parts of a complex number.

3. Perform addition, subtraction, multiplication, and division of complex numbers.

4.Simplify expressions involving the imaginary unit i

5.Represent complex numbers on the Argand (complex) plane.

6.Determine the modulus and argument of a complex number.

7.Convert between rectangular and polar forms.

8.Apply De Moivre’s Theorem to powers and roots of complex numbers.

9.Solve mathematical problems involving complex numbers in various contexts.

SUGGESTED LEARNING RESOURCES

a)Textbooks and Reference Materials

Stewart, J., Redlin, L., & Watson, S. (2015). Precalculus: Mathematics for calculus (7th ed.). Cengage Learning.

Sullivan, M. (2020). Algebra and trigonometry (11th ed.). Pearson.

Kreyszig, E. (2011). Advanced engineering mathematics (10th ed.). Wiley.

Brown, J. W., & Churchill, R. V. (2014). Complex variables and applications (9th ed.). McGraw-Hill Education.

b)Online Learning Platforms

Modules

Module 1: Introduction to Complex Numbers

(i) The need for complex numbers.

(ii) The imaginary unit i.

(iii) Standard form a+bi.

(iv) Real and imaginary components.

Module 2: Operations with Complex Numbers

(i)Addition and subtraction.

(ii)Multiplication.

(iii)Division using complex conjugates.

(iv)Powers of i.

Module 3: Graphical Representation

(i)The complex plane.

(ii)Plotting complex numbers.

(iii)Distance from the origin.

(iv)Geometric interpretation of operations.

Module 4: Polar Form, Modulus and advanced applications

(i)Modulus of a complex number.

(ii)Argument and angle measurement.

(iii)Conversion between rectangular and polar forms.

(iv)Trigonometric representation.

Introduction to Linear Algebra

Course Description

This course introduces learners to the basic concepts of linear algebra. It focuses on vectors, matrices, and systems of linear equations, and how they are used to solve real-life and mathematical problems. The course builds a strong foundation for further studies in mathematics, engineering, and technology.

Learning Outcomes

By the end of this course, learners will be able to:

  1. Define vectors, matrices, and linear equations.

  2. Solve systems of linear equations using different methods.

  3. Perform basic operations with matrices.

  4. Apply linear algebra concepts to solve simple practical problems.

Core Topics

  1. Vectors and Vector Operations

    • Definition of vectors

    • Vector addition and scalar multiplication

  2. Matrices and Matrix Operations

    • Types of matrices

    • Addition, subtraction, and multiplication

  3. Systems of Linear Equations

    • Solving using substitution and elimination

    • Solving using matrices

  4. Applications of Linear Algebra

    • Real-life applications

    • Problem solving using vectors and matrices

Sample Interactive Activities

  1. Discussion Forum:
    Learners introduce themselves and share where linear algebra is used in real life.

  2. Practice Quiz:
    Short quizzes on vectors and matrix operations with instant feedback.

  3. Problem-Solving Assignment:
    Solve systems of linear equations and submit answers.

  4. Group Activity:
    Learners work together to solve a real-life problem using matrices.