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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Write_Mikey_Write!

a day 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

a day 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.

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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.

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.

July 3, 2019 at 12:15am

#961956

Unlucky

What is your go-to dish to bring to a potluck? Does your family have any traditional recipes? (In Hawaii, these appetizers are called “pupus” )

The predominant religious denomination around here is Southern Baptist.

I think most people, when they think "Southern Baptist," they think, like, Jerry Falwell - intolerant, closed-minded, racist, sexist, homophobic, etc.

While I think all these things, I also think "casserole." Intolerance aside, until they find out I'm not Christian, they're quite welcoming - I present as a straight white guy. Well, to be fair, I am straight, though not narrow. And to be even more fair, not everyone embodies all of the negative traits of the Southern Baptists as a whole. Many of them are, I presume, good people. Anyway, point is, from this outsider's perspective, the Southern Baptists are obsessed with casserole.

One thing that SBs do very well, apart from attempting to inject their religion into our government, is potlucks. And since, as I said, they're the predominant religious denomination around here, I've been to what passes for parties among them. They'll call a potluck at the drop of a hat: weddings, funerals, random church functions, some Puritanical law gets passed in the state, whatever. At these parties, you can be sure of exactly two things:

1) Myriad varieties of deviled eggs;
2) Myriad varieties of casserole.

Personally, I think the "deviled eggs" thing is psychologically interesting for a bunch of religious folks, but there's really no mystery about the dish itself: take hard-boiled eggs, remove the yolks, combine the yolks with various other ingredients, cram the resulting mixture back into the hollowed-out hard-boiled egg whites, and top with what passes for fiery spice around here (usually paprika).

Casseroles, however, mystify me. I'm not sure why. They can't be that hard to do, or millions of Southern Baptists wouldn't do them, in all their various incarnations. You'd think that would teach them something about variety and the wonders of diversity, but... no. They just plop down their armies of Corningware, oblivious to the obvious metaphor.

It's not like I've never made a casserole - I've followed several recipes. But what stumps me is that I don't know what the essential thing is that makes a casserole a casserole and not something else. Baking? You also bake lasagna; is that a casserole? Meat? Nonsense; there are plenty of vegetarian casseroles.

My parents were, obviously, not Southern Baptists. I don't think the Jewish congregations around here have a tradition of potlucks; we're more the "caterers" type. I wouldn't know, though, because I quit being religious before I bothered to care about such things. And my parents were from diametrically opposite cultures in the US, so they didn't even have food in common. Add to that the simple fact that my mother couldn't cook worth a damn, and my dad didn't (product of his time, you know), and pretty much everything I know about food I taught myself in self-defense.

There is one thing that my mom could cook, and that's chicken soup. But I'm pretty sure that's a genetic thing, passed down from Ashkenazi to Ashkenazi in a line of matrilineal descent.

Soup, however, doesn't usually feature at potlucks. Too messy. And I never quite got the hang of it, myself. So, yeah, no traditional family recipes here. Just stuff I've picked up along the road.

So, when it comes to the ultra-rare potluck that I end up crashing, I go with the easy out: chips and dip. One time I forgot the dip, and apparently that's a massive social faux pas, because I never got invited back.

Suits me. It's not like they agree with my alcohol-positive lifestyle.

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