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 8 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 10 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.

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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.

January 19, 2024 at 1:28pm

#1062664

The Once and Future Cheese

It's snowing again here. Not too heavily, and it's not really sticking on the roads, but every time people in Virginia see so much as one flake of snow, it's like some alien invasion, as if they've never seen it before. And it snows here. Every. Winter. Well, not so much last winter, but every other winter. And I had to leave the house, so I got to experience the chaos firsthand.

Anyway, no need to leave the house again until tomorrow evening, so I get to share with you this article from Eater about...

When Cheese Can Tell the Future
The Kitchen Witch brings the ancient art of tyromancy — divination through cheese — to the modern day

Headline notwithstanding, no, cheese cannot tell the future. Unless it's moldy when it's not supposed to be, in which case it predicts its own journey to the trash can or compost pile.

Still, people think it can, and that's fascinating to me.

Throughout history, people have sought answers about the unknown.

Yes. That's why there is science. Do you know how milk becomes cheese? Well, neither do I, beyond the absolute basics, but science does.

But predicting fates and futures hasn’t always been synonymous with tarot cards and oracles; sometimes, it comes down to what you eat or drink.

With me, it's like, "I see a night on the toilet in your future."

Though each society has its own versions of food divination, shape interpretation is the common ingredient in countless fortunes told. In the 1700s, “pulling the kale” was a popular way to predict the qualities of one’s future mate based upon the traits of the pulled-up plant.

And people think kale sprung suddenly onto the scene in the noughties.

And then there’s tyromancy, or cheese divination.

Oddly enough, the word "tyro" means novice or amateur, but that's from a different root word.

And now, Jennifer Billock, the Chicago-based creator of the Kitchen Witch newsletter, is taking this ancient yet new-to-most form of fortune telling into the 21st century with group readings. “It seemed like a fun way to tell fortunes that also ended up being delicious,” she says.

As long as I get to eat the cheese afterward, I'll pretend to believe in divination.

After the introduction is an interview between the publication and Billock. I'm not going to quote from that, but it goes into the mechanics of how it's done (short version: she reads the "variations," like mold stripes or ridges at the break of a hard cheese).

As with astrology, I'm amazed at the amount of work and thought people put into things like this. Sure, I don't accept that dairy products (or stars) can actually tell one's future, but I've come to the understanding that life is a little more fun with these absurdities than it would be without them.

Still, the only future I can predict when I have a hunk of cheese is that it will soon be in my belly.

2 Like • Comment • View 4 comments

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