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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10 Most Recent Blog Comments:

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').

1 Like

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

1 Like

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

November 4, 2021 at 9:10am

#1020795

Hide-And-Seek Champions

I vaguely remember when they posted grainy pictures of missing sprogs on milk cartons. I liked to call them the Hide-And-Seek World Champions, because I'm an asshole.

PROMPT November 4^th

We've all heard of people who mysteriously 'go missing'. Tonight, write about a person who 'goes missing'. Someone that you read about in the newspaper or online, but nobody seems to know them, or remember them.

But of course, anyone (not just kids) "going missing" is a serious matter. Sometimes it turns out to be a misunderstanding. Often, especially with older kids or adults, they seem to disappear (I mean, they know where they are) because they want to. Most of the time, with kids, it's another family member; on occasion, it's an actual case of "stranger danger."

And I think most of us have noted a certain bias in local and international reporting when it comes to missing people. Specifically, attractive young white women get all the attention (as with everything else in life), while everyone else is, at best, mentioned somewhere between the obituaries and detergent ads or, at worst, never.

This is not just observation bias on our part, either; someone did an actual study.

I'll call Missing White Woman Syndrome MWWS here. Honestly, the only thing about the study that surprised me was that the disparity they found seemed less than I expected. But that's why we do science - to try to systematically eliminate subjective biases.

The latest example of this was Gabby Petito, who the news just. Would. Not. Stop. Talking. About. And I don't even watch cable news, or have cable; I just caught the edges of the stories here on the internet, and that was enough to make me wonder what real news they were distracting us from. I mean, sure, the case had sensational elements, but I just couldn't help thinking it was an obvious instance of MWWS.

On Maui, a few years ago, this chick

went missing, it made national news, everyone was freaking out about it, and fortunately it ended relatively well. But earlier the same year, these dudes

disappeared. You've never heard of them. Hell, the link I just posted is Maui local news.

Or right here in my town, a hot blonde chick, Morgan Harrington, disappeared from a Metallica concert like 12 years ago now. I don't know; maybe you remember this one, too. Hell, Cosmopolitan magazine did a bit about it, with the headline, and I'm including the link here so you know I'm not joking in any way, A Beautiful Girl Gone Missing

. I mean, you expect "beauty" language from Cosmo, I suppose, but what in the acid fuck does it have to do with anything?

Especially since a couple of years later, Sage Smith disappeared from another part of Charlottesville. Never heard of her? Not surprised. Marginalized trans woman. To their credit, the cops continued to work the case, and from what I can tell it ends just as tragically (though it certainly took a lot longer), but as far as I know, it didn't receive national attention at the time.

Now, I'm not saying that missing human cases must always be treated equally. There are always going to be some more salacious, or mysterious, or disturbing than others -- which was part of the reason for the constant focus on Gabby Petito. Several thousand people "go missing" every year (the exact number depends on definition), and that's a lot to follow. If someone is missing, and there's a chance the public can help, sure - but why make a hiker's disappearance on Maui national news, for instance? It's not like you might accidentally run into her unless you happen to be walking around Hale'akala.

I'm also not saying any missing person case is trivial. All I am saying is that all human life has value; sure, it's worse when kids go missing because they're not as self-sufficient, but everyone who goes missing is going to be missed by someone -- by definition.

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