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.

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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.

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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.

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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
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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.

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September 4, 2023 at 10:43am

#1055136

Astronomy

It's Labor Day here in the US, and I have an aversion to labor, so today's comments will be brief.

The 8 Best Astronomy Books For Beginners
From Mary Roach’s hilarious look at space travel to astronaut Scott Kelly’s photos documenting a year off planet.

Usually, Atlas Obscura highlights interesting locations here on Earth. This represents a bit of an expansion of their purview.

It’s easy to forget amid summer road trips and back-to-school to-do lists that our Earthly home is just a floating speck of blue in the vastness of the universe, that our human lives are just a blink in our galaxy’s long history.

It should be easy to forget. No matter how insignificant we may seem, we're the ones figuring this shit out, and that's pretty awesome.

Even if you’re completely new to the topic, these books are accessible, moving invitations into the furthest reaches of our cosmos.

I'm anything but new to the topic, but one cool thing about astronomy is that there's always more to learn.

I haven't read any of these books. They seem interesting enough, though they're not all technically about astronomy.

Since there's not a lot of point to copying the book titles and summaries—they're right there in the link, and the summaries are elevator-pitch length—this is as good a time as any to do one of my language investigations.

Before astronomy, there was astrology. Astrology is, rightly, considered pseudoscience at best, complete horseshit at worst. I fall somewhere in between; I look at it the same as I view folklore. It's an interesting window into psychology and human history.

Which leads me to the language bit. Other legitimate branches of science use the -ology suffix: psychology, biology, geology, zoology, etc. It can also be used to describe questionable fields of study, like theology, demonology, or UFOlogy, perhaps lending these subjects a false aura of science. The suffix itself, obviously, comes from the Greek "logos," which as I understand it just means "word" (which doesn't explain why a "logo" is often just a pictogram).

Astronomy is different, then, in the use of the "-nomy" suffix, which, according to the usual sources, means something like arranging or categorizing. But it's not alone. You also have taxonomy, which has nothing to do with paying the government money and everything to do with categorization; economy, which is notoriously slippery to define; gastronomy, which is kind of related to today's link because Atlas Obscura also hosts Gastro Obscura, a series of articles about the wonders of food (I've linked those a few times); and not many others. Anomy, however, refers to a lack of moral or ethical standards, which, what? It's also spelled anomie because English is had to pin down, sometimes.

Had the history been different, perhaps "astrology" would be the science while "astronomy" would be the folklore. We'll never know. But one reason I can't fully dismiss astrology as a subject is its place in history. Even Newton, known for his discoveries in science and mathematics, started from a foundation of astrology and alchemy. Just to be clear, though, I don't "believe in" it; I just find it interesting, same as with the folklore surrounding cryptids.

Astronomy can be defined as the study of celestial objects, and this is why it's kind of fuzzy to define in practice: Earth is, itself, a celestial object. One of my favorite websites, which I've visited nearly every day since it began in 1995 and which hasn't changed format much in those nearly three decades, is the Astronomy Picture of the Day

—and it often features images of Earth alongside investigation of faraway planets, stars, nebulae, and galaxies.

Which leads me back to the original link, because some of the books there are really about Earth. And that's okay; our -ologies and -onomies are all interconnected, anyway.

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