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:

Brandiwyn🎶

a day ago
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 9, 2023 at 9:11am

#1057044

I Am The Law

I didn't fact-check any of these. It's just something fun from Cracked.

5 Laws Designed to Screw Over One Guy in Particular

One person does something bad, and so we pass a new law, to forbid anyone else from trying that same thing. That may not be the most thoughtful path toward creating a legal code, but it’s a routine way of doing things.

Which is how you end up with laws like "No baton twirling within 20 feet of park benches." Introduced at the last city council meeting by an elected official with a bandaged head.

Sometimes, though, when we pass a reactive law, we’re not worried about that crime becoming a trend. We just want to keep our thumb on that one guy.

As far as claims to fame go, you could do worse than "inspiration for a law."

5. Ohio’s Urine Collection Law

Part of their pee-nal code.

In 2008, a 56-year-old man named Alan David Patton was caught collecting urine from a bathroom in a park in Dublin, Ohio.

Okay, ew.

Authorities charged him with criminal mischief. This broad and ill-defined law landed him a maximum of 60 days in jail, which really didn’t seem enough for this weird freak. So, they came up with a new law. Ohio now made it illegal for anyone for to collect “bodily substances without consent and for non-medical purposes.” The new penalty for this new crime? Six months in prison.

Urine trouble now.

4. The Right to Detain Greg

Australian man Greg Kable stabbed his wife to death in 1989. Not cool, Greg.

In case it's not clear, wife-stabbing was already illegal in Oz.

The sitting Parliament passed a new order called the Community Protection Act. If a prisoner due for release was deemed a danger to the public, said the order, they would keep him in prison until they were satisfied he wasn’t... Fortunately for all future prisoners, New South Wales amended the act to limit its scope. Now, it would only apply to Greg Kable, specifically.

"Whataya in for, mate?" "Being Greg Kable."

3. Banning One Kid from Talking About Grass

This one's way more interesting than just that bit.

Sometimes, this made sense. For example, a 26-year-old was brought up for repeatedly playing “Do They Know It’s Christmas” to annoy his neighbors, an offense that ought lead to life in prison.

Nah. 20 years, max. Life sentences should be reserved for "Simply Having A Wonderful Christmastime."

An ASBO from 2003 forbade an 87-year-old man from being sarcastic to his neighbors.

I'd be boned.

2. An Anti-Armstrong Law

The burgh of Langholm in Scotland has a law on the books that says any Armstrong who enters the town must be hanged.

Maybe we should arrange a bicycle race through there.

The Armstrong was Johnnie Armstrong, who lived in the 16th century. The English remember him as a criminal due to his habit of raiding England, while the Scottish remember him as a folk hero, due to his habit of raiding England.

That quote by itself was why I had to blog about this article. Bonus, though:

We’d probably never know about this old law. Except, in 1972, Langholm received a famous visitor: astronaut Neil Armstrong.

"We must obey the law. Quickly, now, hang... a portrait of Neil Armstrong in the museum!"

1. The Man Who Worked His Butt Off

This one's a stretch (pun absolutely intended). It's not really a "law."

As of 2016, Britain’s National Health Service had a certification for something called a “rectal teaching assistant.” This was someone employed by the government to visit medical schools, so doctors in training could learn how to conduct prostate exams by practicing on his well-documented body.

And I have no doubt he was the butt of many jokes. Rectum? Damn near killed 'im.

And with that, I'm done. If I were more ambitious, I'd double-check all these, but more importantly, I'd try to find examples from outside the English-speaking hegemony. I'd bet Germany has some fun ones, for example.

7 Like • Comment • View 2 comments

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