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!

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.

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.

October 1, 2019 at 12:01am

#967052

Locavore

https://narratively.com/lessons-from-a-local-food-scam-artist/

Working summers at an authentically quaint roadside produce stand, a teenage salesperson is schooled in the not-so-subtle art of how to con a foodie from the big city.

I'm gradually coming to the realization that some people are just asking to be scammed out of their money.

I met my first New York foodie over twenty years ago, when I was seventeen, hawking “local bananas” at a roadside produce stand in rural New Jersey.

For instance, anyone who believes that bananas grow in New Jersey. If you believe that, I have a bridge to sell you, and it's even closer to your apartment.

But “local” was the magic word hand-painted on our signs; it was what made our customers, most of them New Yorkers driving to country vacation cottages, slam on their brakes and pull over.

Now, I could make jokes about growing anything in New Jersey, but I'll refrain. It's not like the whole state is the Northeast Corridor, which looks like the set for the next Fallout game. Parts of it are actually kind of nice.

Still can't grow bananas there. Oh, I suppose you could get a couple of bushes, or trees, or whatever started in a greenhouse, but you're not going to get the volume needed for sales.

“Give me Jersey peaches over Georgia peaches any day.” Those were Georgia peaches they were palming to their kids, whispering, “eat up,” before the fruit had been weighed and paid for.

More evidence that it's perfectly okay to scam some people out of their money: they're stealing from you.

“I wait every year for the real Jersey tomatoes. You can’t get that country flavor in the city!” They couldn’t get it here, either: These were New Mexican beefsteaks, greased with mineral oil to an enticing sheen and petroleum fragrance. Didn’t they notice the absence of any roses-and-resin tomato-y perfume?

Well... it is New Jersey.

The foodies argued. “But I bought local Silver Queen from the stand down the road last week!”

I said, “The stand down the road is lying. Local Silver Queen won’t ripen till August.”

They didn’t believe me. They couldn’t bear the challenge to their connoisseurship.

Or maybe - bear with me on this - they're experiencing various cognitive biases, and have put up walls against contradictory information.

Their quest for authenticity didn’t stop there. They asked me, “What are you people doing here? Last year, an American owned this stand.” He still owned it. He had hired me – an Asian-American who didn’t look the part of the rustic local – and a bunch of other kids for the summer. One New Yorker opined, “I’ve been summering here since I was a kid, but people like you keep coming here and buying up the local businesses.” They wanted to know where I came from, originally, and how selling them melons fulfilled my American Dreams. None of the other employees got these questions. Perhaps I spoiled the New Yorkers’ nostalgia for the countryside. To some of them, my provenance was far more suspect than that of the produce.

But I've been assured that racism only happens here in the South.

They never even learned that, if you hector a nonwhite teenager about displacing white people’s jobs, she’s going to hide rotten tomatoes in the bottom of your bag.

Trolling level: epic.

So, when my boss’s son put up the “local bananas” sign, I let it alone. A few foodies laughed. A few questioned me accusingly: How could the bananas be local? “Greenhouses,” I said one day. “Miles and miles of greenhouses. In Andover Township.” The word “township” got them; it was so quaint.

See? Greenhouses. I told you. Also, for the unaware, "township" (usually abbreviated as "twp" on signs) is what they call certain municipalities in NJ. It's just a technical term, like "village" or "city." You'd think New Yorkers would know that, but they tend to be oblivious to everything on this side of the Hudson.

For a long time, I despised New Yorkers.

You know why I believe you when you say you're from New Jersey?

Anyway, since the 30DBC is over, I'm back to snarking on semi-random internet articles, and this one just happened to be in my queue.

3 Like • Comment

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