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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 10 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 12 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.

February 27, 2024 at 11:32am

#1064998

Olive It And More

To wrap up February's "Journalistic Intentions"

[18+]...

Olive

There's a grocery store on Broadway, on the Upper East Side (corner of 80th Street if you're ever in the area) called Zabar's.

I get the impression that it's moderately well-known across the land. Maybe it's been in a movie or show or two; I don't know. Maybe its vibe, which more modern and chain-affiliated places can't replicate with their corporate policies, focus on metrics, and eventual enshittification, is just something people respond better to.

Since I haven't been there in a while, I can't comment on their prices, but I remember them being about what you'd expect in Manhattan: slightly elevated, though not sky-high like in Hawai'i. But their location means they serve a moderately well-to-do clientele, which means offering some premium selections. The first time I went in there, I nearly dehydrated salivating over the seemingly endless, though really not because we're still talking about a Manhattan grocery store with limited space, selection of cheeses.

And then I saw the olive section and almost fainted from delight.

I like olives, you see. Not just black, green, and kalamata, but all olives.

Want to hear my most idiosyncratic quality? I don't think I've ever admitted to it in here before. Or anywhere online, really. I usually keep it to myself, because the one time I told someone in person, the look I got was so filled with horror and disgust, you'd think I made a habit of munching on baby sandwiches.

I get green olives on my pizza.

That's right. Pizza. New York slice, of course, with, at minimum, pepperoni and onions... and green olives.

I can't be alone in that, even if no one else will ever fess up. If I were, the local pizza shop wouldn't offer it as a topping, would they? And not just the local pizza shop, but the old one, the one that had been around since before I even got to town in 1983, the one that even more closely approximated NY pizza but sadly went out of business because of, well, you know—they offered green olives on their pies, too. Not just because of me, either; it was on the menu when I first visited each of them. Every once in a while, someone will misread the order slip and give me green peppers, which are an abomination, instead of green olives. But usually, they get it right, and they've never been out of stock (to be fair, the whole reason for green olives is preservation, so the little eyeballs might have been sitting around for years, for all I know).

Last time I went to pick up my extra cheese-pepperoni-onion-beef-jalapeno-green olive pizza at the place that managed to stay open, I recognized the owner as the one who provided the pie to me. "Ah, good! Green olives!" he enthused in his boisterous, Brooklyn-Italian accent. "You have wonderful taste!"

Finally, vindication.

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