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.

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.

January 3, 2022 at 12:15am

#1024067

Up in Smoke

Well, it finally happened - computer froze up as I was previewing an entry, so it got lost. The following represents a half-arsed effort at recreating what I was saying.

Another "JAFBG"

[XGC] entry. Probably going to do this all month.

Talk about something that's illegal, but not morally wrong in your opinion.

A bit over 100 years ago, in 1920, the US passed a Constitutional amendment prohibiting the use, sale, transportation, import, etc. of alcoholic beverages (or words to that effect; you can look it up easily enough).

If you're not familiar with the US system, suffice it to say that a Constitutional amendment is a high bar to clear. You might have heard the expression, "It would take an Act of Congress," used when something is very, very difficult to get approved. Well, passing an Amendment makes an Act of Congress look like a walk in the park.

And yet, in a rare example of a meeting of the so-called minds on both Left and Right, they managed, and for the next 13 years, the country sank deep into the Hell that was Prohibition. During those dark times, far more social harm was done by Prohibition than was ever done by allowing people to just fucking drink in peace.

The only valid response to an immoral law is to work to repeal it, and that's what finally happened (there might have been other factors involved).

So it is today with cannabis.

While several individual States here have legalized it, it remains prohibited at the national level, so it fits the prompt. I've never been a big consumer of it, myself -- can't say I've never done it, though -- but that's immaterial; prohibiting it goes against everything this country is supposed to stand for. And to have it be illegal when other substances, including tobacco, sugar and, yes, alcohol, have the potential do to far more harm just seems stupid to me; besides, I don't accept the idea that laws should protect people from themselves, only other people.

Just get over yourselves and legalize it, already. Oh, sure, go ahead and put age limits on it and tax it like we do with booze, and no, people shouldn't drive under the influence -- but that's a completely separate issue and I resent that Prohibitionist groups have largely succeeded in swaying public opinion by conflating the two.

Yes, I'm writing this from a US perspective; I'm aware other countries have already legalized it. But I live here, so I'm most familiar with US laws.

And I had more to say, but like I noted above, I lost my original entry here, so that's going to have to do it for now. Hopefully tomorrow I'll be more careful.

7 Like • Comment • View 3 comments

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