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!

a day 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

a day 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.

August 3, 2019 at 12:14am

#963641

Humans.

Today, I'm going to wade into a minefield.

https://www.theatlantic.com/family/archive/2018/06/imagining-a-better-boyhood/56...

In hindsight, our son was gearing up to wear a dress to school for quite some time. For months, he wore dresses—or his purple-and-green mermaid costume—on weekends and after school. Then he began wearing them to sleep in lieu of pajamas, changing out of them after breakfast. Finally, one morning, I brought him his clean pants and shirt, and he looked at me and said, “I’m already dressed.”

Don't care.

He walked the half block to school with a bounce in his step, chest proud. “My friends are going to say dresses aren’t for boys,” he told me casually over his shoulder. “They might,” I agreed. “You can just tell them you are comfortable with yourself and that’s all that matters.”

Beginning to detect the faint, familiar odor of bovine excrement.

When he walked into his classroom, sure enough, one child immediately remarked, “Why are you wearing a dress? Dresses are for girls.” A teacher swiftly and gently shut down the child’s commentary and hugged my son tightly.

Ah, yes... homegrown fertilizer. Teachers don't hug, nowadays. They get investigated and fired for that shit.

One day when my husband dropped him off, he heard a little girl stand up to a naysayer and shout, “Boys can like beautiful things, too!”

Sure he did.

Thing is, though, possibly bullshit anecdotes aside, the author makes, in my opinion, excellent points.

Maybe you weren't expecting me, a middle-aged man, to say that. I'm supposed to be the Enemy here, trying to hold on to antiquated ideas of gender norms in the face of a rethinking of everything that "gender" means.

Fuck that.

Like I said, I don't care - one way or the other.

Thing is, though - I don't always understand. I feel like there's a subtext to every conversation about sex and gender that I'm not a party to; I'm not even invited to the party. Maybe that's because, like I said, I'm a middle-aged man and thus subject to the social expectations thereof - in short, I'm put in a box as much as anyone else is. Maybe it's because, when I was a kid, my parents were progressive enough not to put all those "this is what boys do" crap in my head. Probably it's something else entirely; I don't know, because whatever it is, I'm missing it.

But it doesn't matter. I don't have to understand why some penis-owners insist that they're women, or the other way around; I just have to accept it - or not. I do accept it, because, clearly, it happens. I don't have to understand why anyone does anything, for that matter, and as long as they're not hurting anyone else in the process, I find it difficult to give a shit.

Way I see it, everyone - everyone - has stereotypical "masculine" and stereotypical "feminine" traits, likes, and dislikes, in varying degrees. As with most social things, it's not binary, but on a continuum. For instance, I know a guy whose hobby is collecting vintage Barbie dolls and making little dresses for them. I know another one who likes to enjoy a "Princess Cake" for his birthday every year, complete with pink flower frosting. Not that it matters, but both these people identify and present as men, and they've each been married (to women) way longer than I ever was; I only say this to point out that their other traits are in no way stereotypically effeminate.

So, I don't know what I'm missing about this conversation. People like what they like. To shame them into not liking something is basically making it clear that you don't accept them as a person, to attempt to suppress their expression of creativity or joy or whatever.

And that sucks, no matter who you are.

Therefore, I keep reading about it, and I attempt to have conversations about it, but I feel like every time I bring it up, someone decides I'm not, I dunno, ideologically pure enough to even have the discussion with, and I'm left even more bewildered than before. Just let people be who they are, is my view - again, excluding those who want to do harm; I'm not advocating, say, letting pedophiles have their way. Or, maybe they don't know who they are; in which case, let them explore.

Anyway, yeah, I know I'm rambling. That happens when I can't quite wrap my head around something. Maybe someone else can shed some light on the subject for me.

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