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.

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.

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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.

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.

January 25, 2024 at 8:36am

#1062941

Appropriate

Cultural appropriation!

How Kosher Wine Became a Hit in the Caribbean and Beyond
Manischewitz has a historic consumer base not only in the Caribbean, but also in African-American and East Asian communities.

...no, not really cultural appropriation. Mani was the first wine I ever had, which should surprise no one. I can't remember the first beer I ever had. The first beer I ever finished was a Red, White, and Blue, and that didn't end well at all.

Growing up on the Dutch Caribbean island of Curaçao, 34-year-old Diahann Alexandra Maria Atacho’s parents would regularly turn to an unexpected beverage when they wanted something “special to drink.” They’d pull a bottle of Manischewitz—a brand of incredibly sweet wine well-known to American Jews—and serve it in a crystal wine glass, filled to the brim.

On Pesach, you drink four glasses of wine with the seder meal. Traditionally, these glasses were filled to the brim. My parents never let me do that, though, despite the very clear commandment of You-Know-Who.

Manischewitz has a consumer base not only in the Caribbean, but also in African-American and East Asian communities. Of the over 900,000 cases produced in 2015, some 200,000 were exported, largely to the Caribbean, Latin America, and South Korea. What is most surprising is this is not a new trend.

I'm not sure about "surprising." Lots of things transcend their original culture. I drink Scotch, and I'm not Scottish. I eat sushi, and I'm not Japanese. Last week, I did those things at the same time. Sure, Manischewitz may not be, objectively, a great wine, but it's accessible to people without the taste for more French-style wines.

The reason for the beverage’s sweet—some might say sickly—taste is due to the grapes used to make it. By the 20th century, immigrant Jews were producing kosher wine from cheap, hardy, and sour Concord grapes from the American Northeast. Adding significant amounts of sugar made it drinkable.

It's also far from the only fortified wine in existence.

The article delves a bit into the history, then:

Horowitz argues that the Great Migration to northern cities may have exposed African Americans to Manischewitz, which became known as “Mani.”

Which is at least a more respectful name than what happened to that other Jewish winemaker, Mogen David, who put out MD 20/20 and had it promptly called Mad Dog.

Lots more history at the link. I'll just wrap up by saying that cultural exchange is a good thing, especially when it comes to delicious fermented and/or distilled beverages. But also food. Pretty much everyone eats, and we're sharing a planet here, so why not share the food (and wine)?

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