Complex Numbers (Book)

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Complex Numbers

Complex Numbers

A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number.

The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi.

Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary.

Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty.

http://www.ddewey.net/mandelbrot/

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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 15 hours ago
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

about 21 hours ago
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

a day ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

a day ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

Dec 26, 2024 at 10:00am
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

February 24, 2024 at 10:04am

#1064779

Nerdy Words

Everyone knows that we nerds are generally immune to problems affecting normal people, such as STDs, sunburn, and athletic injuries. To make up for it, we have today's article, from Cracked:

5 Diseases That Only Hit Nerds

You may, however, come down with a whole series of other specialized conditions that will savage your body or will break your mind.

And no, one of them isn't "brain overheats from exertion."

Disclaimer: everyone is a nerd about something. This article is about the classic nerds who follow intellectual pursuits far more than is socially acceptable. Like me, for instance.

5. Nobel Disease

This isn't the same thing as noble rot.

When you get a Nobel Prize, the world is telling you you’re one of its smartest people. You may be set for life. So, there’s always the possibility of the recognition going a little to your head. Winners might go on to pursue ideas unconnected with their specialty, sometimes devolving into total nonsense.

First of all, this doesn't apply to the Peace Prize, which hasn't been relevant for decades. Second, I don't think anyone I know is in danger of contracting this dread malady. And finally, this just goes to show that even geniuses aren't immune from the Dunning-Kruger Effect. Which may not actually be a thing, but I say it is because I know better than They do.

4. Laptop Thigh

If your skin spends lots of time next to a heat source, you may come down with a condition called Erythema ab igne. That’s Latin for “redness from fire.”

One way English is superior to Latin is that we use single-syllable nouns for the most common things, such as cat, heat, and red. And nerd.

Many gentleman nerds already now the dangers of keeping laptops on their actual laps (it fries the testicles), but laptop thigh can affect anyone.

There aren't too many advantages to being a short guy. You're locked out of the dating pool—wait, no, that's an advantage. Another advantage is you don't have a lap, so "laptop" isn't the right descriptive. It does merge two simple one-syllable words, but, for instance, mine is always on a desk or table when I use it. Still, better than the French version: ordinateur portable.

3. Formaldehyde Hunger

People tend to become hungry in the close vicinity of corpses. This is dubbed “formaldehyde hunger,” on the assumption that the preserving chemical formaldehyde gets into people’s systems and stimulates their appetites.

I thought they mostly quit using formaldehyde, switching to a less carcinogenic preservative. But what do I know?

2. Brain Fag Syndrome

No, this isn't about a common slur for nerds, gays, and gay nerds.

The British diagnosed this syndrome in their subjects in Africa, who continued to use the term into the 20th century. Over in America, though, people doing lots of brain work were also experiencing mental fatigue. Some doctors dubbed this an exceptionally American problem, naming it “Americanitis.”

Nowadays, I'm pretty sure "Americanitis" is used for an inordinate love of firearms, eagles, and eagles bearing firearms.

The best treatment, they note, is rest. Yes, you feel better when you take a rest from work. These past 150 years of medical research have produced some marvelous breakthroughs.

This is as close as the list gets to "brain overheats from exertion."

1. Dysrationalia

English words for uncommon things are allowed to be multisyllabic, and derived from Latin and/or Greek.

When we’re measuring brain power, you’ve got your computational power, but then you’ve also got your ability to be rational, and this consists of a bunch of different types of intelligence. There’s reflective cognition. There’s epistemic rationality, your ability to make correct decisions free of various fallacies. There’s syllogistic reasoning, which requires discarding biases. Put it all together, and we find that some people with high I.Q.s score worryingly low in rationality. We describe such people as suffering from dysrationalia.

In other words, you can be really smart and still be really stupid. As anyone who's read my blog can attest.

5 Like • Comment • View 2 comments

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