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 24, 2022 at 12:04am

#1025259

Clawless

And another one I can't fully answer from "JAFBG"

[XGC]... but I'm going to try anyway.

Channel your inner Seinfeld and tell us the most petty reason you've broken up with someone or lost interest in dating them.

I don't know, because I haven't broken up with, or dated, anyone except my most recent ex-wife since Seinfeld was originally on TV (you don't want to know how long ago that was; it was longer than you think and you'll feel old). I wasn't the one doing the breaking-up, usually, and the few times I did the reasons were eminently justifiable and not at all petty.

No, really.

No. Really. Stop laughing.

(Stupid canned laugh track.)

There was one time in the 90s when I dated this one chick, briefly. She was nice but incurious, and desperately wanted children while I desperately didn't. But that wasn't why I broke up with her (I was just very, very careful to never let the condoms out of my possession).

No, I broke up with her because she declawed her cats.

Like I said, not a petty reason. Though some might find it to be so. She certainly did. I consider it to be an inexcusable, barbaric practice which usually only serves to protect one's precious, precious furniture.

There are other ways to protect the furniture besides mutilating cats. And even if there weren't, a living thing's welfare is almost always more important than that of furniture. (One exception: cockroaches.)

It's not that I didn't know her cats were declawed when we started getting serious. It's just that I wasn't aware, at first, of how horrible it was, thinking it was only slightly bad and you just couldn't let the cats outside, which wasn't an issue for her at the time because she lived in an apartment. The internet was in its nascent stages back then, populated mostly just by nerds like me -- long before Failbook, before Wikipedia, even before WDC. (Did you know Writing.com predated Wikipedia? By about four months. Now you do.) But I started digging around on there and became appalled.

There really wasn't anything I could do about the poor kitties. She treated them well enough otherwise, and unlike in civilized countries, declawing isn't illegal in the US. But I just couldn't see the relationship going anywhere because a) I will always have cats, b) I will never have them declawed, and c) that was all I needed to know about her priorities.

And don't get me wrong -- I may be a little judgey on this subject, but I never hated her for it; I wished her well and moved on. She wasn't so cool with the breakup, though, so, unlike with most of my exes, I have no idea where she is or what she's doing (but I am certain based on discussions with mutual friends that the condoms, indeed, worked as designed). Since it's been about 25 years, the cats in question have long since gone to meet Bast. It was simply a sign for me that we were, ultimately, incompatible.

Hell, if she got what she wanted in life, she's got fully grown kids by now. I just hope she didn't declaw them, too.

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