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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Write_Mikey_Write!

about 8 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

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Adherennium Plotting something

about 10 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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.

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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.

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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.

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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.

June 24, 2022 at 12:02am

#1034172

Everyone Calls Me Mushroom Because I'm Such A Fun Guy

Want another reason not to go outside?

7 Poisonous Mushrooms and What Happens if You Eat Them
If you forage for mushrooms, these are some you’ll want to leave in the woods

("But Waltz, if you hate the outdoors so much, why are you linking to Field & Stream?")

("Shut up.")

There is a commonsense rule about wild mushrooms that all outdoorsmen should heed: Avoid them.

As much as I despise the entire idea of common sense (more on that is coming at a later date), I have to admit that in this case it's right. Not just for outdoorsmen, either. Indoorsmen like me. Outdoorswomen. Outdoorsnonbinaries. Whatever.

There are about 10,000 species of fungi out there, of which only a small number will kill you.

Unless, presumably, you're in Australia, where everything is trying to kill you.

As an aside, I've known several people who just plain won't eat mushrooms. Can't stand the taste, the texture, or both. Which is not to say that they couldn't be poisoned by something else. Me, I get my shrooms at the grocery store like God and nature intended.

Often, as in the case of the aptly named death cap (Amanita phalloides), they look like a hundred other mushrooms, some of which are delicious.

Which is aptly named? The common name, or the scientific binomial, which obviously comes from the root "phallus?" ("Both.") Lots of mushrooms are dick-shaped (for various species of dick). That's kind of their brand.

Got a friend who “knows” mushrooms? Great! Just remember that you’re trusting this person with your life and that experts get poisoned, too.

As far as I'm concerned, there are people knowledgeable about fungi. Some of them even moreso than me. But when it comes to putting something in my mouth, well, no one's an expert.

Here are some mushrooms you definitely want to avoid.

Any that don't come from a well-regulated grocery store or pizza place. Farmer's markets don't count. Vegan pop-ups definitely don't count. Your meth supplier does, though, because she's got a vested interest in keeping you alive so you can buy more meth.

Seriously, though, the article includes helpful pictures, and I'm only going to hit the highlights here.

1. Death Cap, Amanita phalloides

It's right there in the name, people.

Famous people who may have died from eating death caps include the Roman emperor Claudis (54 A.D.) and Holy Roman Emperor Charles VI in 1740.

The morel of this story is: don't be roamin'.

Ah, the rare double pun. Pretty proud of that one.

You know, it just occurred to me that this article could double as a guide to How To Kill Someone and Get Away With It.

2. Fly Agaric, Amanita muscaria

This is the one you see in fairytale books with a bright red cap and white spots.

I don't think this one should necessarily be included in the list. While it's not the kind that you'd get from your meth dealer, it has, historically, been used for... you know. Trips. Still, deaths have been associated with it, usually due to overdose, accidental or otherwise. Then again, deaths have been associated with water, too.

Still not picking any up off the forest floor.

3. False Morel, Gyromitra esculenta

This mushroom looks like the human brain, not a morel.

So you're saying it's a... morel hazard?

Look, this one is so ugly (you'd have to look at the article to get the full effect) that I don't know why anyone's trying to eat it in the first place.

4. Autumn Skullcap, Galerina marginata

With a name like that, I'm picturing the cartoon skull you see hovering over characters that have just died.

As a rule of thumb, avoid anything with “skullcap” in the name.

Good advice there. If only it would self-label with its name, like in a video game.

5. Alcohol Inky, Coprinus atramentarius

They’re fine by themselves and absolute living hell if you have booze with them.

Well, I'd be boned.

6. Deadly Webcap, Cortinarius rubellus

If you’re a fan of kidney or liver failure, this is the way to go.

I promise you, there are far more fun ways to experience kidney and/or liver failure than venturing into the not-so-great outdoors and picking shrooms.

7. Ergot, or Spurred Rye, Claviceps purpurea

In a 1976 article in Science Magazine, author, LR Caporael theorized that an outbreak of ergotism caused by Claviceps purpurea may have been the cause of the strange behavior that led to the execution of 20 men and women in the 1692 Salem witch trials.

I'd heard this. It may even be true. The fact remains, though, that "strange behavior" is no reason, on its own, to execute a person. Either way, this isn't one that someone would likely eat on purpose, or mistake for a different but edible fungus.

The really interesting thing about ergot is that, as bad as it is, it's formed the basis for pharmaceuticals.

In general, however, the advice given at the beginning of the article holds true: if you're tempted to pick up and eat a wild mushroom... don't. Makes me wonder how they figured out that some mushrooms were edible in the first place.

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