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.

July 26, 2021 at 12:01am

#1014334

No Choice

Tomorrow will be the final "JAFBG"

[XGC] prompt. Today, I'm going to break with my own tradition and piss off some people.

Sometimes it's frustrating to have to bite your tongue. This is your chance - get up on your soapbox and rant. What do you wish you could say to someone (or a lot of someones)?

Lately, I've seen a few stories in the news about people who had the opportunity to get the covfefe vaccine, didn't, and ended up in dying, in pain, intubated and alone, in the hospital.

And my shits-to-give reservoir has run completely dry. In fact it's inverted, and when I see a story like that these days, all I can think of is, "Good. One less stubborn, willfully ignorant idiot in the world."

I saw where one 20-something dude got the 'rona and received a double lung transplant. This pissed me off all the way to Mars, because those donor lungs could have gone to someone more deserving than someone who refused to get a little shot in his arm when all the information was out there that it's a good idea to do so, but he only listened to things that tickled his confirmation bias. Those donor lungs could have saved the life of a coal miner, an asbestos-snorter, or a three-pack-a-day chain smoker -- anyone more responsible than this dipshit.

Now, look, ordinarily I don't care what you do to yourself. Drink? Great. Smoke? Fine. Do a few lines of coke until your heart explodes? You do you. Point a loaded gun to your head and fire? Well, I feel bad, but ultimately it's your choice. It only affects you. Sure, some people will be sad for a while, but you could have thought of that first.

But this shit going around is stealthily contagious, way worse than "the flu," and there are worse outcomes than dying, intubated and alone, in the hospital - like living for a few more years with scarred lungs, dealing with other organ damage, or losing your sense of taste and smell. And there are people who, for whatever reason, cannot get the shot and are therefore vulnerable; the more people get their shots, the less vulnerable they are. "But it doesn't affect kids!" Not as much, no, but some still die or suffer worse consequences from it, and more, they have the opportunity to pass it on like a retarded game of Telephone. Not to mention the reservoir of active viruses that have all the more opportunity to mutate into something more contagious or deadlier, like it's already done at least four significant times.

It's not like wearing a seatbelt or not. I personally don't give a shit if you wear a seatbelt. Doesn't affect me. This is more like drunk driving: Please, by all means, drink all you want, but the minute you take off drunk in your car you're endangering everyone else.

So what I wish I could say to a lot of someones is: Get the goddamned motherfucking vaccine. I know you're terrified of needles. I get it. I'm terrified of shit touching my eyeballs, but I'm going to suck it up and get eye surgery anyway, and that's not even affecting other people (again, unless I'm reckless enough to drive without corrective lenses).

I mean, surely it can't actually be the vaccine that's making you cower like a little kid in a dark scary room, is it? That shit's safe. It's safer than most medications. It's safer than goddamned sugar, and you eat that shit all the time. All the shit you've heard about nanobots, DNA alteration, mind control? That's deliberate disinformation. Stop believing obvious bullshit.

And if you don't -- if you still refuse to believe the science (not me, the actual science) -- if you're able to get the vaccine and you refuse to do so -- and I read about you in the news dying in an ICU, you know what I'm going to do?

I'm going to laugh my goddamn ass off, that's what I'm going to do.

And if you whine about "I should have gotten the vaccine!" like I've seen some of these people did, I'm going to laugh even harder. I might even burst a blood vessel and die from laughing so hard. It's okay; I'll go to oblivion knowing I literally had the last laugh.

I'm done feeling compassion for these morons. I'm completely over having a live-and-let-live philosophy when it comes to this shit.

"But you can get the vaccine and still get sick!" Yes, it's not perfect, but it gives you a better chance, and reduces opportunity for further transmission.

"But I had the disease and all I got was the sniffles!" Lucky you. Get the shot anyway. It provides better protection than having had the 'rona.

"I have a friend who said their second cousin's mother's boyfriend was laid up in bed for three days after the second shot!" Still better than 'rona. I got a shingles vaccine a while back. Two-shot regimen. Second shot knocked me on my ass for two days. Still beats getting shingles. Second 'rona shot just made me tired for a day. My anecdata is just as good as theirs. Better, because it's first-hand.

"Hell with it. If I get it, I get it." Again, fine, I wouldn't care if it were just about you. But it endangers others. If you don't care about some abstract "others," I mean your family and friends.

"People have gotten the vaccine and then died!" Yes, they have, but correlation isn't causation. I know someone who died shortly after getting married. Therefore, marriage will kill you and should be avoided at all costs! Even if some of them died from the vaccine, your chances are still better than if you catch the damn virus.

"My body, my choice!" Oh, NOW you believe that? Right. Also, no, like I said, it's not just about you.

"It's all a liberal hoax perpetrated by the lamestream media to force us to comply with government overreach!" Please die slowly and painfully, hopefully before breeding.

At this point, there's no excuse to not get the shot if you're eligible and it's available.

And yet...

I don't want to have this much schadenfreude. I know that while we're responsible for our actions, we can only choose what we're programmed, by genetics and environment and experiences, to choose (reading this rant counts as "experience," by the way; I'm not saying people can't change their minds). There really is no choice at all, so should I really be celebrating these anti-vaxxer deaths and injuries? Sure, they're influenced by bad actors in a lot of cases, but those influencers don't have a choice, either. But... by the same logic... I also don't have a choice.

I'm all out of shits to give.

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