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:

Brandiwyn🎶

a day ago
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').

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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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 22, 2023 at 10:30am

#1046836

The Best Offense

There are a few more prompts for me to pick from at random in this incarnation of "JAFBG"

[XGC]. This is one of them:

Tell us about a time when someone else's humour offended you.

I gotta admit, this is a tough one. I'm not one to get offended at a lot of things, and most of the things I do find offensive aren't jokes. Like when someone doubts that I know how to drive a manual transmission vehicle. Dude, I was driving a four-speed truck around the farm at 12, as soon as I could reach the pedals and see over the dashboard simultaneously, and my first five vehicles were all manual. I only drive an AT now because a) "standard" isn't standard anymore, or much less expensive, and b) back problems make it difficult to clutch on a regular basis. But I promise you, if I wanted to steal your piece of shit car, your stick-shift isn't going to deter me.

Certainly, general things exist that offend me. Censorship, for example. One of the things I like about this website is that we're not censored, only content rated. You want to write scat torture porn? Go right ahead. It's probably going to be XGC, but nowhere are you guaranteed an audience.

But I don't much like to talk about the few things that do offend me. This is because trolls tend to use it against me. Like, let's use a fictional example. Say I'm offended by, I dunno, birds. If someone feels like trolling me, that would give them a hook to do so. They could send me pictures of birds, leave dead birds on my doorstep (don't do that; it's my cat's job), sign me up for the Audubon newsletter, whatever.

Which brings me back around to jokes.

Now, this is where I wish we had better graphics capability here. Picture a 2x2 grid, like a Punnett square

in genetics. Along the top you have the joker's intention: "Meant to offend" and "Didn't mean to offend." Along the side you have the recipient's attitude: "Doesn't look for offense" and "Looks for offense."

Now, as with the biology behind the Punnett square, in reality, things are more complicated, nuanced, and shaded, but I feel like these are the main categories. Let's look at them one by one.

"Meant to offend" x "Doesn't look for offense" - the recipient might not even realize that the joker was trolling, and might even be inclined to give them the benefit of the doubt. This, hopefully, takes the wind out of the joker's sails.

"Didn't mean to offend" x ""Doesn't look for offense" - usually not a problem.

"Meant to offend" x "Looks for offense" - oh, boy, is this wonderful for the joker/troll. They got exactly what they wanted: a rise out of the listener/viewer.

"Didn't mean to offend" x "Look for offense" - once called out, the joker will probably be apologetic. But it won't matter, because they'll be smeared all over social media for their inadvertent offense, even if they apologize afterward.

Whatever the case, the best way to handle these situations is to not assume the worst of the joker. If the person is particularly offensive, a simple explanation of why they're being offensive is a good way to start. Like "Hey, look, some people might take offense at your suggestion that we should run over bicyclists when they're on the road." If they continue to make jokes about scoring points for hitting bikers, then you know they're trolling and should be shunned.

Well, I've already banged on long enough, and I still can only remember one time when a joke actually offended me. As it was offensive to me, and not funny, I don't remember many of the details, but it went something like: a missionary knocked on a door, and an atheist answered. The missionary calmly told her about Jesus, and she went to slam the door in his face, but something kept the door from closing. She went to slam it again, still wouldn't close. Finally, the missionary said, "You might want to move your cat out of the way."

Like I said, not funny. But the way it was told (again, I can't remember it exactly) was in the standard format of a "joke." But look, I've been studying and practicing humor for decades, and I can't find anything funny about this. Is it an example of what passes for humor in evangelical circles? I know some evangelicals, and they have a sense of humor, so I don't know.

Is it trying to say that the atheist is blind to what's right under their noses? If so, they've got that backwards.

Is it a rag on cat people? That's one of the things that can offend me, so it's not only not funny, but deliberately hurtful.

Not to mention that jokes about hurting animals aren't funny in the first place.

But like I said, no point broadcasting my reaction for all the world to see (until now, when it becomes relevant as the response to a prompt). Just file it under "reasons not to engage with door-to-door religion vendors."

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