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.

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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 15, 2023 at 10:11am

#1055769

Going Bananas

It's a promo on LitHub for a book, but whatever. We're all readers here. And it tracks with what I already knew.

How the Banana Came To Be—And How It Could Disappear
Emily Monosson on the History, Evolution, and Biological Enemies of a Staple Fruit

Yesterday, I bought some bananas, and noticed that since the summer, they had doubled in price!

...from 12 cents each to 24.

(This is one reason you have to beware of that sort of emotional language when you encounter it.)

I still find it difficult to believe that a banana's actual worth, a couple thousand miles from where they're grown, is less than a quarter. I'm sure there are all sorts of subsidy shenanigans going on, and low-paid workers involved, but I can't be arsed to research it.

Bananas are a fruit that unites the world.

Not so sure about that, but as fruits go, they're definitely one of the easiest. Peel and eat, no messy juice, no seeds. I saw a video once where a creationist took that and ran with it as "proof" of intelligent design. Well, they were intelligently designed, all right: by intelligent humans, who genetically engineered a seed-infested fruit with very little meat and turned it into a snack as easy to eat as a Milky Way bar.

Though there are thousands of varieties, most of us in the western world eat only one: the Cavendish.

Or, as we tend to call them here in the US, "bananas."

Of the twenty-two million tons of bananas exported to the United States, Europe, and Asia, most are grown in Latin America and the Caribbean.

I still remember a brief tour of a banana plantation in Belize. But this article goes into a lot more detail around the growing and shipping process, which I'm not going to repeat here.

The banana plant is easy to mistake for a tree, but it is the largest known herbaceous flowering plant.

This is a distinction much like tomato being, botanically, a fruit.

The plants grow, produce flower and fruit, and die.

Ready-made metaphor there.

The article also goes into the rise and fall of the previous kind of shipped banana, the Gros Michel (commonly translated to English as "Big Mike," but I prefer "Fat Mikey.") That's fairly widespread knowledge now, as is the whispers, going on for some years now, of the soon to be certain demise of the Cavendish.

Hasn't happened yet, but with banana prices doubling here, maybe it's happening?

What the article doesn't get into is whether there's a suitable, fungus-resistant successor to the Cavendish. We can be pretty clever with our bioengineering and selective breeding, so I expect they'll find a way. Otherwise, based on the numbers in this article, a whole lot of people are going to find themselves unemployed.

And, worse, I'll have to find another easy fruit to like. And that, for me, holds no ap-peel.

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