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

March 21, 2021 at 12:02am

#1006785

Put a Pin in This Synergy

I thought about writing this entry in ironic corporatespeak, but I can't bring myself to do it.

Forgive Me, For I Have Sinned ... Against The English Language

Look, the English language isn't exactly pure as driven snow.

They're unavoidable — corporate buzzwords and gobbledygook.

Oh, they're avoidable, alright - you just have to be old enough to retire.

Belittled and unloved, corporate jargon endures, even thrives. There is no movement to rip down the wallpaper. And let's be honest fellow desk jockeys. Not only have we heard these words and phrases. We've probably used them ourselves.

Even worse than the author's use of corporate jargon are the atrocities committed against the English language in that paragraph.

The use of jargon is often tied to where people stand in a social hierarchy, according to a new paper from three social scientists... People with less prestige in an organization are more likely to use buzzwords. Like interns, new hires and first-year students.

Oh, it was in a paper; it must be true.

She makes a distinction between useful jargon in specialized fields such as medicine, science and law — and the workplace language so prevalent today, a hybrid of business school lingo and Silicon Valley hype. The latter, she says, is littered with "BS words — like orientate or guesstimate, or omnichannel or core competency."

To be fair, "orientate" is probably just fine in Britain, and "core competency" might actually have real meaning. The word "guesstimate" has been around for at least 45 years, and I have hated it for 50 of those years. Make a guess. Or an estimate. Pick one.

Okay, so apparently "guesstimate" has actually been around since the 1930s. That doesn't mean we can't make it stop if we really wanted to.

Let's take a word that suddenly became popular a few years ago: efforting. On the surface it sounds ridiculous.

Let's dig a little deeper... nope, it sounds ridiculous below the surface, too. But we English speakers love to verb nouns, and then gerundize the resulting verb. I remember when "parent" was strictly a noun, for example.

To quote the great sage Calvin, "Verbing weirds language."

On a more consequential scale of slippery is the word "synergy," a longtime favorite of corporate executives extolling the benefits of mergers.

And this really pisses me off, because "synergy" is a great word with a specific meaning. But like many other words, it's been beaten into oblivion by oblivious idiots.

Being able to complain about language changes is one of the many perks of getting older, along with joint pain and ragging on "kids these days." But I've always hated corporate jargon, and did my best not to practice it when I was running a company. I should have had a swear jar, except it'd be called a jargon jar. While swearing in a professional setting is generally frowned upon, buzzwords are far, far worse offenses.

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