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:

Write_Mikey_Write!

about 2 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.

1 Like

Adherennium Plotting something

about 4 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.

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.

August 18, 2021 at 12:02am

#1015798

Shaka, Brah

There are many things in this universe that I don't understand -- there are, in fact, a lot more of them than there are things that I do understand -- but way up near the top of the list of things I don't understand is "fashion."

Hawaiian shirts are now “problematic” symbols of colonialism

But one thing I do know: Nothing says "I don't understand fashion" more than a Hawaiian shirt. Which is why they're a central feature of my wardrobe.

This article has been waiting in my queue since April, so some things in it may seem outdated -- unlike Hawaiian shirts, which never go out of style.

To make matters worse, this is kind of a rabbit hole of links. I'm linking to a blog I follow. He links to the original Guardian article and a couple of other sources. If you've been here long enough, you'll know that I'm certainly not above linking directly to the Guardian. But in this case, I find Coyne's commentary more interesting.

Oy! I wake up this morning to find, thanks to the Guardian, that my beloved Hawaiian shirts—technically, “aloha shirts“—have gotten the stink-eye from the Perpetually Offended. According to the paper—or rather, according to a Princeton academic, clearly empowered to be an arbiter of culture, these colorful shirts, worn by locals (Asians, Native Hawaiians) and immigrant mainlanders alike, are now “problematic.”

Translation: someone didn't like seeing them, so they dug around for reasons to try to cancel them. Dig deep enough, and you can find a reason to be offended by any given article of clothing. Hawaiian shirts just make great targets -- mostly because you can't miss them.

To get the full argument, you'll have to go to the link. He quotes from a few different sources, and I don't want to confuse anyone by pulling excerpts from excerpts. It's more Coyne's own conclusions that are important here.

But it gets worse, for the white-supremacist “Boogaloo Boys“, who advocate revolution, have adopted the aloha shirt as an unofficial uniform.

To me, that's just another reason to wear one: to reclaim the shirts from those assholes.

Frankly I don’t give a rat’s patootie about what Anishanslin or any other Pecksniff thinks. I don’t wear my aloha shirts with camo pants, body armor, or weapons, so I’m not worried about accusations of being a proud boy.

I mean, as they are the height of fashion, it's no surprise that different groups will gravitate toward them. Should we also cancel ties because hedge fund managers wear them? No, we should avoid them because they've outlived their usefulness. Unlike Hawaiian shirts.

This fracas about aloha shirts is a prime example of performative wokeness: pretending you’re engaging in helping the downtrodden while actually doing noting to help them—what you’re doing is singling yourself out as particularly moral and perspicacious.

Coyne's love of big words exceeds only my own.

You know, it used to be that people would rag on cheap shirts from Squall-Mart or similar places. "Those are made by near-slaves making a dollar a day! We should boycott them!" Well, it's good to be concerned about the plight of the workers of the world. It's even better to actually do something about it. Boycotting the shirts isn't doing something about it. In fact, I'd argue that if everyone stopped buying those shirts, those workers would cease being workers, and instead of making a dollar a day they'd make no dollars a day. That's unrelated, though; my Hawaiian shirts, the ones I bought for myself anyway, are actual USA-made shirts stitched up in actual Hawaii.

The point being that you can have opinions all day, which is fine, but are you actually helping?

I was once at a local bagel place, and I happened to overhear a conversation about food as cultural appropriation. I'm fine with hearing arguments about it, though I'd argue that it's really not except in very narrow circumstances -- but in this case, the person doing the arguing was eating a bacon, egg and cheese bagel.

Why that's hypocritical, I hope I don't have to explain.

In conclusion, you can pry my Hawaiian shirts from my cold, dead hands. And then hopefully give them to someone else who appreciates these pinnacles of sartorial elegance.

Alamo had a special screening of this fantasy adventure quest movie from 1982; I hadn't seen it in a long time, so I went.

One-Sentence Movie Review: The Dark Crystal

No CGI, no frenetic pacing, no jump cuts, no catering to people with short attention spans; this slow-paced movie focused on plot and character design, so it's probably not going to appeal to modern audiences, but taken in the context of the time it was produced, it's a showcase of creativity.

Rating: 3.5/5

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