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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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').

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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

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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

September 13, 2023 at 8:29am

#1055696

Hammer and Advil

One of my favorite tropes is the mad scientist who, when no one believes them, tests the creation on themselves. In stories, that rarely ends well. In real life... well, it usually doesn't end well there, either. But here's an exception... sort of.

The Inventor of Ibuprofen Tested the Drug on His Own Hangover
Stewart Adams’ headache subsided—and his over-the-counter pain reliever became one of the world’s most popular medications

A hangover cure—that is, a real one, not the folk remedies like "mix a raw egg with last week's coffee grinds" nonsense—is one of the most important inventions one can make. This is not only because it pisses off the puritans who get apoplectic when someone's not punished for having a good time, but that's a huge bonus.

In retrospect, perhaps toasting the success of a new medication he helped invent with several shots of vodka in Moscow was not a good idea.

Are you kidding me? That would be epically awesome! Well, not while there's a war going on over there, but any other time.

English research scientist Stewart Adams was faced with the consequences of his actions: a serious hangover.

But what if there doesn't have to be consequences?

He reached for that new drug and swallowed a 600-milligram dose.

For reference, most OTC ibuprofen comes in 200mg tablets, and the usual dose is 2 pills for 400mg. I've been prescribed as much as 800mg by dentists and the like. So this is not outside of the realm of sanity, mad scientist trope aside.

Stewart Adams and his associate John Nicholson invented a pharmaceutical drug known as 2-(4-isobutylphenyl) propionic acid. It was later renamed ibuprofen and is now one of the world’s most popular nonsteroidal anti-inflammatory drugs (NSAIDs)...

Sadly, my doctor insists I shouldn't be taking NSAIDs unless they're prescribed. She had no comment on my drinking, though.

Stewart Adams began his career in pharmaceuticals at the young age of 16, when he started an apprenticeship at a drug store owned by Boots UK Limited, then known as Boots the Chemist. He went on to earn a degree in pharmacy at the University of Nottingham and then received his PhD in pharmacology at the University of Leeds.

Looks like he was one of the most British people to ever Brit.

Now if someone could explain to me why they call that other pain relief medicine acetaminophen here, but paracetamol over there, that'd be great. I can't be arsed to look it up.

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