Introduction to Complex Numbers and Quaternions

This is a course that will teach about complex numbers and their basic operations before going into quaternions, quaternion operations and eventually quaternionic rotations.

The goal of this course is just to get something out there in the Mathematics section of ureddit that focuses specifically on complex numbers and interests people in complex numbers, as well as hopefully teaching those with a fair bit of knowledge on complex numbers/quaternions something new.

Lectures
1. Lesson #1 - Terminology, Addition and Subtraction of Complex Numbers

This lesson goes over exactly what it says in the title. Feedback is appreciated, let me know if you have any questions.

Side note, I may end up combining the 2nd and 3rd lessons.

2. Lessons #2&3 - Multiplication, Division, Magnitude, Argument and Polar Form

Combined lessons 2 and 3 because lesson 2 ended up being fairly short. Goes over multiplication and division, then into the magnitude and argument, which are used to put a complex number into polar form.

Feedback appreciated, questions welcome.

3. Lesson #4 - Real Roots of Complex Numbers

Sorry it's kind of later in the day than usual that I'm uploading this.

This lesson goes over finding square roots and nth roots of any complex number.

4. Lesson #5 - Euler's Formula, Complex Powers, Exponentials, and Logarithms

Euler's Formula lets you do some cool stuff.

5. Lesson #6 - Introduction to Quaternions

Covers terminology, addition and subtraction. Fairly short lesson.

Prerequisites

This course is for absolute beginners, so there are no specific prerequisites. All you'll need is some basic knowledge on trigonometry - really just how the cosine, sine and tangent functions relate to a right triangle.

Syllabus

Class material will be hosted online in pdf format. The first lesson will be uploaded on October 24th of 2014 and lessons should be posted each Sunday from then on.

The bits that say "tangent lessons" aren't terribly relevant to the main focus of this course, which is operations on complex numbers and quaternions, but are instead lessons on alternative methods of representing complex numbers and quaternions in interesting ways. If they are posted, they won't interfere with the rest of the lesson schedule and won't be posted on a Sunday.

COMPLEX NUMBERS

Lesson 1~

``````Introduction to complex numbers and the basic terminology

Representation using i as the square root of -1

Real and imaginary parts, conjugate

Complex plane

Subtraction
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Lesson 2~

``````Multiplication

Division
``````

Lesson 3~

``````Magnitude, argument, polar form

Multiplying in polar form
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Lesson 4~

``````Real roots
``````

Lesson 5~

``````Euler's formula

Exponential, natural logarithm, one complex number to the power of another
``````

Tangent lesson?

``````Alternative representations of complex numbers

Ordered pairs with addition and multiplication formulas

2x2 real matrices
``````

QUATERNIONS

Lesson 6~

``````Introduction to basic properties of quaternions

Basis units

Noncommutative multiplication

Scalar and vector parts

Conjugate

Brief lesson on addition and subtraction
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Lesson 7~

``````Multiplication
``````

Lesson 8~

``````Division

Norm

Reciprocal
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Lesson 9~

``````Exponential, logarithm, one quaternion to the power of another

Polar form
``````

Lesson 10~

``````Quaternionic rotations
``````

Tangent Lesson?

``````Alternative representations of quaternions

4-part vectors with addition and multiplication formulas

4x4 real matrices, 2x2 complex matrices

Cayley-Dickson construction
``````