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 14 hours ago
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 ✍️

about 17 hours ago
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

about 20 hours ago
In response to "Gray Matters"

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

2 Like

tj-Merry Mischief Maker

a day ago
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

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

May 3, 2024 at 11:31am

#1070468

It's a Crime

I'll do another one from "JAFBG"

[XGC] today:

What issue do you think has been misrepresented?

Since I pick these at random, I didn't have an axe to grind in mind when I landed on this prompt. It took me a while to sift through all the issues I could remember from relatively recent news stories, eliminate from consideration those that are too divisive to deal with in the short time I take to write these things, and decide on one I gave enough of a shit about to comment on.

An AI could probably have done that faster, and indeed, I considered doing this entry on AI, perhaps even using AI (which is not actually AI, but that's a semantic bugaboo for me and a whole different level of misrepresentation).

Since I was in NYC last week, though, I decided on crime.

No, I don't mean I decided to pursue a life of crime. English is sometimes ambiguous like that, which can be annoying but can also lead to great amusement, so let's not change that anytime soon. What I mean is, I think crime is an issue that's been misrepresented in media, both social and commercial.

The reason I mention NYC above is that there's this pervasive attitude that "big city" crime is a huge problem, and in the US, there's no bigger city than New York. And yet, the reality is, though I can't be arsed to look up statistics, that most of NYC is pretty damn safe. Sure, crime happens... but it can happen anywhere, and if you're a victim of assault or mugging or whatever, the prior chance of you being a victim of assault or mugging or whatever is largely irrelevant.

Discussing this issue is made difficult by how one defines "crime" as well as other factors. Different localities have different priorities. In my experience, law enforcement makes a big show of drug busts, while mostly ignoring crimes with actual victims, such as burglary (yes, drug use is often a bellwether for other crimes, but that doesn't mean it is, by itself, worse than, say, sawing off someone's catalytic converter).

Mainly, though, the issue comes down to one of familiarity. As an analogy, most people in the US drive nearly every day, while they only fly occasionally. The dangers of flying are thus magnified in a person's mind, sometimes to the point of actual fear of getting on an airplane. Statistically, though, it's clear that you're much safer on a jet (even if it was recently made by Boeing) than you are driving to and from the airport. Likewise, someone from a medium-sized town like mine might be wary of the Big City with all its reported crime, while being used to the risks in one's hometown.

Similarly, when it comes to threats to your family, other family members (or former family members) are much more likely to be the problem than some stranger.

And then you get the politically-charged rhetoric about letting in immigrants and the like, who, according to the opponents thereof, are either lazy and want handouts, or are so willing to work hard that they're taking all our jobs; either way, though, they're perceived as potential criminals, which ignores all the US-born criminals who are much more likely to be the ones who do you some harm.

It's understandable to be concerned for one's safety. And it pays to take reasonable precautions. But listening to the media might give a person a warped view of where the actual threats to it are coming from.

3 Like • Comment • View 2 comments

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