<h1 id="imaginary-numbers">Imaginary Numbers<a aria-hidden="true" class="anchor-heading icon-link" href="#imaginary-numbers"></a></h1>
Imaginary numbers exist.
The name is unfortunate. When they were proposed, someone used the term "imaginary" to make fun of it, and the name stuck. They could have just as easily been called something less whimsical, like "auxiliary" or "orthogonal" numbers. But they are as real as negative numbers or fractions are.
Negative numbers let you solve <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x+2=0</annotation></semantics></math>x+2=0, whereas imaginary numbers let you solve <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mn>2</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x2 + 2=0</annotation></semantics></math>x2+2=0.
Imaginary numbers and real numbers are the two starting sets that when combined make up complex numbers (ie. complex numbers are the union set of all real numbers and all imaginary numbers.

Imaginary Numbers

thoughts-on


Welcome to my Second Brain! Here you'll find thoughts, lessons, facts and any other interesting musings that I've come across or thought up over the years. A lot of what I have gathered is originally from the minds of others, while some of it originates from myself. Some notes may contain misinformation, though I try to be rigorous with my additions.

What I have here does not necessarily reflect my thoughts and views. I collect information not based upon whether I agree with it or not, but rather when I determine it to contain some value that can be served in the future.  

You can think of this collection of inter-linked notes as my personal wiki.

This Dendron notebook is the sister vault to the tech-focused [Digital Garden](https://tech.kyletycholiz.com)

## Tags
Throughout the Second Brain, I have made use of tags, which give semantic meaning to the pieces of information.

- `ex.` - Denotes an *example* of the preceding piece of information
- `spec:` - Specifies that the preceding information has some degree of *speculation* to it, and may not be 100% factual. Ideally this gets clarified over time as my understanding develops. I try to go back after I have better understood the topic and clear out the notes of `spec:` tags
- `anal:` - Denotes an *analogy* of the preceding information. When I can, I attempt to link concepts to others that I have previously learned.
- `mn:` - Denotes a *mnemonic* to aid in memorization
- `expl:` - Denotes an *explanation*

## Resources
### UE (Unexamined) Resources
Often, I come across sources of information that I believe to be high-quality. They may be recommendations or found in some other way. No matter their origin, I may be in a position where I don't have the time to fully examine them (and properly extract notes), or I may not require the information at that moment in time. In cases like these, I will add reference to a section of the note called **UE Resources**. The idea is that in the future when I am ready to examine them, I have a list of resources that I can start with. This is an alternative approach to compiling browser bookmarks, which I've found can quickly become untenable.

### E (Examined) Resources
Once a resource has been thoroughly examined and has been mined for notes, it will be moved from *UE Resources* to *E Resources*. This is to indicate that (in my own estimation), there is nothing more to be gained from the resource that is not already in the note.

### Resources
This heading is for inexhaustible resources. 
- A prime example would be a quality website that continually posts articles- another example would be a tool, such as software that measures frequencies in a room to help acoustically treat it.
