Complex Numbers - Mathematical Methods (Undergraduate Advanced)

Do you want to learn how to work with numbers that go beyond the real line? Do you want to understand the concepts of imaginary unit, conjugate, modulus, argument, and polar and exponential forms of complex numbers? Do you want to master the skills of performing algebraic and geometric operations on complex numbers using different methods and tools? If you answered yes to any of these questions, then this course is for you! In this course, you will learn how to: - Define and classify complex numbers and their real and imaginary parts - Perform addition, subtraction, multiplication, and division of complex numbers using the standard form a + bi - Find the conjugate, modulus, and argument of a complex number and use them to compare and simplify complex numbers - Represent complex numbers on the Argand plane and visualize their geometric properties and transformations - Convert complex numbers from rectangular to polar and exponential forms and vice versa - Use De-Moivre's theorem and Euler's formula to find the powers and roots of complex numbers in polar and exponential forms - Use complex numbers to define and manipulate trigonometric and hyperbolic functions and their inverses - Use complex numbers to define and manipulate logarithmic functions and their properties - Use complex numbers to graph and solve equations of circles, lines, and other curves on the complex plane This course is suitable for anyone who wants to learn or review the basics of complex numbers and their applications. It is especially useful for students and professionals in engineering, physics, computer science, cryptography, and other related fields. By the end of this course, you will have a solid understanding of complex numbers and their operations. You will also be able to apply the knowledge and skills you gain to real-world problems and challenges that involve complex numbers. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

34 hrs

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
MTH 202: Mathematical Methods II
MTH 202: Mathematical Methods II
Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

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MTH 101: Elementary Mathematics I - Algebra and Trigonometry
MTH 101: Elementary Mathematics I - Algebra and Trigonometry
Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

Master the foundational mathematical structures essential for success in quantitative undergraduate degrees and professional technical roles. This comprehensive learning track delivers a rigorous treatment of algebra and trigonometry, moving rapidly from fundamental set theory and real number operations to advanced topics including matrix algebra, complex numbers, and analytical trigonometry. You will establish the critical problem-solving framework required for advanced study in calculus, engineering mechanics, and data science. This programme is primarily designed for first-year university students in STEM disciplines requiring strong analytical bases, particularly engineering, physics, computer science, and economics. It also serves as an intensive, high-level refresher for professionals returning to academia or shifting into data-driven roles demanding precise numerical literacy and logical structuring. Prior competence in standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of core definitions. Upon completion, you will possess the skills to construct rigorous logical arguments using set theory and mathematical induction, model complex relationships with functions and matrices, and analyze periodic systems using advanced trigonometry. You will demonstrate competence in solving diverse equation types, from quadratics to linear systems, and manipulating complex numbers in engineering applications. This track prepares you directly for the mathematical demands of second-year university studies and technical professional certification exams.

See more

Course Chapters

1. Introduction
4
1
Natural numbers, integers, rational numbers, real numbers, and an introduction to complex numbers and their descriptions.
Concept Overviews
4 Lessons
1:23:49
Problem Walkthroughs
1 Lesson
14:45
2. Algebra of Complex Numbers
6
3
Operations on complex numbers; conjugates of complex numbers and their properties; equality of complex numbers.
Concept Overviews
6 Lessons
1:44:23
Problem Walkthroughs
3 Lessons
2:08:34
3. Complex Numbers on the Argand Plane
4
2
Geometric representation of complex numbers on the Argand plane; modulus of a complex number; general and principal arguments of a complex number.
Concept Overviews
4 Lessons
1:44:48
Problem Walkthroughs
2 Lessons
1:29:15
4. Polar Form
5
2
Polar representation of complex numbers; multiplication and division of complex numbers in polar form; powers of complex numbers in polar form (De-Moivre's theorem).
Concept Overviews
5 Lessons
1:15:37
Problem Walkthroughs
2 Lessons
1:30:03
5. Roots
4
4
Equality and roots of complex numbers in polar form.
Concept Overviews
4 Lessons
2:03:40
Problem Walkthroughs
4 Lessons
4:01:13
6. Exponential Form
3
3
Exponential (Euler's) representation of complex numbers; powers of complex numbers in exponential form.
Concept Overviews
3 Lessons
55:21
Problem Walkthroughs
3 Lessons
1:05:01
7. Trigonometric Functions
2
4
Manipulating sines and cosines with complex numbers.
Concept Overviews
2 Lessons
38:38
Problem Walkthroughs
4 Lessons
4:06:38
8. Hyperbolic Functions
1
1
Manipulating hyperbolic functions with complex numbers.
Concept Overviews
1 Lesson
21:29
Problem Walkthroughs
1 Lesson
21:09
9. Logarithmic Functions
1
1
Manipulating logarithms with complex numbers.
Concept Overviews
1 Lesson
22:29
Problem Walkthroughs
1 Lesson
53:19
10. Graphing on the Complex Plane
1
3
Equations in two-dimensional coordinate geometry using complex numbers.
Concept Overviews
1 Lesson
19:11
Problem Walkthroughs
3 Lessons
1:01:16