Pre-Calculus • Series
A Crash Course on Complex Numbers
BL
YL
Yu Heng L
This series ended on September 24, 2021. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
Join me in exploring the interesting world of complex numbers! This short series is intended for students who are new to the area of complex numbers, as well as those who have had previous experience but are looking for a recap.
Each session will consist of short segments on theory, followed by worked examples and Q&A. A homework sheet will be given following each session. Whilst not compulsory, I would encourage you to at least try the problems. Brief solutions will be provided to each problem, but if you would like to go into greater detail with some of the problems, we can go through them during the office hours after each session.
This series covers the fundamentals of complex numbers - we begin the story with their origins and explore their arithmetic. This is followed by an introduction to the polar representation of complex numbers. Lastly, we will delve into how to solve equations involving complex numbers to put what we’ve learnt into use.
Prior knowledge of algebra and basic trigonometry will be required in this course. If you are not yet familiar with trigonometry, you can still attend the first session, but we will be requiring trigonometry from the second session.
Lastly, to keep this series engaging and interactive, I will be asking questions to y’all and I would appreciate your response in the chat. I look forward to meeting you!
✋ ATTENDANCE POLICY
Since this is a short series, there is no strict attendance policy. Do however note that each session builds on the previous, so you may find it harder to keep up if you skip sessions. If many people are unable to make a session, I will consider hosting a makeup session for it.
Dates
August 28 - September 24
Learners
14 / 40
Total Sessions
9
About the Tutor
BL
YL
I'm a high school senior interested in becoming a mathematics educator in the future. My favourite topics are calculus and linear algebra, though I'm willing to learn and teach at all levels. Nice to meet you!
View Yu Heng L's Profile
Upcoming Sessions
0
Past Sessions
9
28
Aug
Cn
Session 1
Complex numbers
Lesson 1: Welcome to the first session! In this session, we will cover:
- Introduction and ice-breakers!
- Origins of complex numbers and the complex plane.
- Addition, subtraction and multiplication of complex numbers.
- Conjugation, its geometric significance and division of complex numbers.
Homework 1 will be issued and should be attempted after this session! If you would like to clarify any doubts about the problems in the homework, there will be office hours for you to do so!
29
Aug
OH
Session 2
Office Hours
Office hours to clarify any doubts you may have about the Lesson 1 and Homework 1.
4
Sep
Cn
Session 3
Complex numbers
Lesson 2: We will move on to discuss any alternate form of complex numbers which is useful later in solving equations. In this session, we will cover:
- The modulus and argument of a complex number.
- The polar form of a complex number and converting between forms.
- Euler's identity and the relationship between exponential and polar forms.
- Operations on complex numbers written in polar form, DeMoivre's Theorem.
Homework 2 will be issued and should be attempted after this session! If you would like to clarify any doubts about the problems in the homework, there will be office hours for you to do so!
5
Sep
OH
Session 4
Office Hours
Office hours to clarify any doubts you may have about the Lesson 2 and Homework 2.
11
Sep
Cn
Session 5
Complex numbers
Lesson 3: We end off this short course by discussing how to solve equations which involve complex numbers. In this session, we will cover:
- Factorising polynomial expressions into linear factors involving complex numbers.
- Solving quadratic equations involving complex roots.
- Finding the nth roots of a number.
Homework 3 will be issued and should be attempted after this session! If you would like to clarify any doubts about the problems in the homework, there will be office hours for you to do so!
18
Sep
Cn
Session 6
Complex numbers
Lesson 4: This is an additional session as we were unable to complete the last set of material during last session. We end off this short course by discussing how to solve equations which involve complex numbers. In this session, we will cover:
- Systems of equations involving complex numbers.
- Finding the nth roots of a number.
Homework 3 will be issued and should be attempted after this session! If you would like to clarify any doubts about the problems in the homework, there will be office hours for you to do so!
19
Sep
OH
Session 7
Office Hours
Office hours to clarify any doubts you may have about the Lesson 3/4 and Homework 3.
23
Sep
C
Session 8
Catchup
Session request for learner.
This is a makeup for lessons 3 and 4 for those who can't make it at a slightly different timing.
24
Sep
C
Session 9
Catchup
Session request for learner.
This is a makeup office hours for those who can't make it at a slightly different timing.