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.

*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.

*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.

*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.

*Lesson #5 - Euler's Formula, Complex Powers, Exponentials, and Logarithms*Euler's Formula lets you do some cool stuff.

*Lesson #6 - Introduction to Quaternions*Covers terminology, addition and subtraction. Fairly short lesson.

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.

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
Addition
Subtraction
```

Lesson 2~

```
Multiplication
Division
```

Lesson 3~

```
Magnitude, argument, polar form
Multiplying in polar form
```

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
```

Lesson 7~

```
Multiplication
```

Lesson 8~

```
Division
Norm
Reciprocal
```

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
```

I look forward to teaching you guys :)

Sorry, no real qualifications. I am certainly well versed enough in this topic to give an internet class according to the syllabus above, but I'm certainly no professor and have not taught professionaly before.

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