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 19 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 21 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 26, 2020 at 12:18am

#976352

What Is Art?

What... is "art?"

https://www.cracked.com/pictofacts-1570-dumb-things-people-misunderstand-about-f...

Dumb Things People Misunderstand About Famous Works Of Art

We all know insufferable people who claim to understand Art with a capital A, and who deliver condescending lectures to the rest of us. But the thing is, sometimes the thing people commonly believe about famous art stuff is objectively wrong.

Nothing profound, deep or intellectually challenging today. Just a fun Cracked link. Also, not much to quote, but I'll share my own thoughts about these. Unfortunately, to understand what I'm saying, you might need to actually click on the link (open it in a new window so you can switch back and forth if you want). If you can't be arsed (or you don't want to open a link that contains a few fine-art boobies), just give this one a miss. I won't mind. Hell, I won't even know.

Also, while Cracked links have thus far been eternal, with the departure of David Wong, who knows how long the site will last? Check these out while you can.

For anyone unfamiliar with Cracked, they have user-generated content from time to time, usually in the form of a Photoshop or caption contest related to a certain theme. This is one of the latter.

30. Yeah, see, the thing about Art is that you can't really control how people use it, copyright issues notwithstanding (memes tend to fall under parody/fair use, but for fuck's sake this isn't legal advice). Witness the chick who did the surreal painting of a pear with a mouth.

29. I say that painting is hanging upside-down. How could one ever tell?

28. Damn. There goes another cherished misconception.

27. I wonder if Theo knew how to pronounce his surname. We certainly can't agree on it.

26. So that's how it is in their family. This makes the Rocky Horror parody even more amusing.

25. Pretty sure that doesn't improve anything.

24. Da Vinci: pioneer of gender studies.

23. Right, because Camembert cheese reminds me of time. As an aside, I own a functioning Melting Clock. Well, it's functioning when I bother to stick batteries in the thing.

22. Probably his neighbor's much larger penis.

21. Thus inspiring fetish furniture for the rest of time.

20. "But the art form was driven by religion rather than juvenile horniness." Hey, it's Rome; why not both?

19. And this is why no one appreciates art.

18. Nope. Definitely aliens. I could go into a discussion of how the modern obsession with aliens is a tech-era upgrade of the older obsession with angels, but a) it would take too long and b) I'm pretty sure I've done it elsewhere.

17. Well, you can see how well that worked out.

16. Actually knew that.

15. Maybe he saw in his mind the pronunciation of his surname, and it made him insane?

14. Why No One Appreciates Art: The Sequel.

13. Picasso was a massive horndog.

12. "Serene moment of life?" That painting always filled me with existential dread, much moreso than Munch's "The Scream," but I would never have figured out that meaning.

11. Either way, I don't get it.

10. Why No One Appreciates Art: Everyone's a Critic.

9. Well, at least they died doing what they loved. Each other.

8. Oh, sure, that's obvious. NOT.

7. Hey, whatever happened to the little girl statue someone put in front of the bull? Oh, someone moved it

, thus changing its meaning because art depends on context.

6. No wonder Charles X is in a wheelchair.

5. You could say it was all a *puts on sunglasses* varnishing act.

4. Personally, I always imagined that statue on a porcelain throne, because I'm actually 12.

3. At least the original one doesn't include Jesus.

2. But WHY?

1. If you scream too long into the abyss, the abyss screams also into you.

I'll just wrap this up by saying I didn't exactly fact-check any of these. They could be utter bullshit. But at least they're amusing.

3 Like • Comment • View 4 comments

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