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 2 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 4 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.

December 20, 2021 at 12:02am

#1023429

Ain't Talkin' 'bout Love

Coincidence that this particular article came up today. You'll see why in a minute.

Eddie Van Halen endured a 'horrifying racist environment' before becoming a rock legend
In an interview with Marc Maron, former bandmate David Lee Roth revealed just how painful the experience was for the late artist, who was of Indonesian and Dutch descent.

It would be very weird if articles appropriate to other topics of the day didn't come up every now and then, but this one's almost eerie -- there are about 40 links in my queue, and this is the only one that I recall with the theme of racism, and it just happens to be right after I saw West Side Story, which also deals with racism and is set in the same general era. You know the story. Movie review at the bottom, as usual.

Anyway, the article.

Music fans around the world are mourning the loss of iconic Van Halen rock star Eddie Van Halen.

Yes, this article is from last year. But considering I'm still mourning Leonard Cohen from 2016, it wouldn't surprise me.

And while many today honor his legacy as one of the all-time greatest guitarists, fans are also highlighting past interviews describing his encounters with painful racism and discrimination because of his mixed race in his early years.

Bit of background for me: I've never particularly liked Van Halen's music. I've never particularly hated it, either. It was just kind of there, on the radio. But I recognize that the band was talented, and that a lot of people were big fans. However, I didn't much care about things like the David Lee Roth / Sammy Hagar spat. I only say this to point out that at no time did Eddie Van Halen's ethnicity matter to me one bit. I mean, from the name, I figured he had some Dutch in there, but my favorite musician also has Dutch ancestry, so I didn't think anything of it one way or another.

And I had absolutely no idea that he was part Indonesian.

Van Halen... was the son of Dutch and Indonesian immigrants and spent his childhood in the Netherlands.

It doesn't take much knowledge of history to figure out how that might have happened.

His former bandmate David Lee Roth, a fellow rock superstar, once revealed on the podcast "WTF with Marc Maron" just how painful the experience was for the young Van Halen and his brother, drummer Alex Van Halen.

I would, however, like to point out that from what little I know about Roth, I'm not sure I'd fully trust anything he said about Van Halen. I suppose they might have reconciled at some point, but again, I have no idea and I can't be arsed to look it up. Still, I don't know why he'd make up something like that, and there seems to be some primary-source confirmation later.

He added that the brothers, who were often referred to as "half-breed" in the Netherlands, still met difficult circumstances after immigrating to the U.S.

I'm not exactly surprised.

"My first friends in America were Black," Eddie told the journalist. "It was actually the white people that were the bullies. They would tear up my homework and papers, make me eat playground sand, all those things, and the Black kids stuck up for me."

I really wonder why he said "actually" there. I mean, that's what I'd expect from racism in the US. Who did he expect to be the bullies? Other marginalized people?

There's not much more to the article, just a few more details which you can see for yourself at the link, but since I didn't know about it I figured other people might not, either. Whether you're a Van Halen fan or not -- and like I said, their music didn't usually do it for me -- you gotta admit that they were talented, and everyone loves a rags-to-riches story.

I just hope that someday, we won't have to hear stories about people being picked on for being different. I doubt it, but I can hope. Even if it did provide the impetus for him to become one of the most famous guitarists in rock.

After all, nothing could have annoyed those bullies more. Living well can be the best revenge, or so they say. I wonder how many of them ended up being fans? "Oh, him, yeah, that's the weirdo we used to shove into a locker at school. Dude can shred!"

One-Sentence Movie Review: West Side Story:

Absolutely gorgeous movie of the Oscar-bait variety (not that the Oscars have been worth a damn for many years), but I'm not sure there's anything new to the story, and the whole "horny teens create unnecessary drama and widespread collateral damage" thing has been played out for at least decades, if not longer.

Rating: 4/5

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