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 6 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 8 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.

May 21, 2021 at 12:01am

#1010505

Cheeses Crust

PROMPT May 21st

Write an open letter to a person or group of people you strongly disagree with and explain why. Use reason not emotion.

Dear Chicago and environs (aka Chicagoland):

That thing you make? With the deep dish and soft bread and thick, gooey toppings?

That's not pizza.

I don't know how you can call it pizza, unless your definition of "pizza" equates to "casserole with bread on the bottom." It's more like a pot pie without a top crust, a crust which is replaced by extra thickness on the bottom one. Pizza -- real, actual, honest pizza -- involves a particular consistency of crust, and fewer toppings than it takes to choke a bear.

Now, don't get me wrong. It can be delicious. I have, indeed, enjoyed the taste of a deep-dish topless pot pie in the past, and probably will again if I can ever make another road trip, or at least find an abomination factory close by.

But it is not pizza.

I know you try very, very hard to distinguish your city from New York, and you mostly succeed. I mean, New York actually has functioning sportsball teams and slightly less crappy weather. But when it comes to pizza, the Platonic ideal comes from a little oven in Queens, run by actual Italian immigrants who only get heart attacks from hearing about how Chicago has mutilated the entire concept of pizza, not from eating said pie.

Oh, well. At least you don't put chili on top of pasta like they do in Cincinnati. But if your entire identity is "at least we're not Cincinnati," you have failed as a city.

Signed,
Waltz
(not an actual Italian)

P.S. California, you're next. Avocado is never an acceptable pizza topping, even if you do get the crust mostly right.

I warned y'all I would do this, and here it is:

A one-sentence movie review of Wrath of Man

While you can't go wrong casting Jason Statham, and the movie has an impressive body count and excellent gunfight scenes, there exists in the film a serious lack of car chases and explosions, two things that can elevate a film from merely good to a cinematic masterpiece.

Rating: 4/5

9 Like • Comment • View 7 comments

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