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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Show Recent Comments

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 18, 2019 at 1:55am

#964364

The Inevitable

Yes, I'm in Vegas. Yes, I'm done indulging my vices for the day. Consequently... blog post. Warning: I've been drinking, so I may say shit I shouldn't.

https://www.vice.com/en_us/article/vbwpdb/the-climate-change-paper-so-depressing...

The Climate Change Paper So Depressing It's Sending People to Therapy
On average, three people read an academic paper. At least 100,000 have read this—and a lot of them haven't taken it very well.

Well, I'm one of those who haven't read it, so let's see what the article has to say about it.

What if I told you there was a paper on climate change that was so uniquely catastrophic, so perspective-altering, and so absolutely depressing that it's sent people to support groups and encouraged them to quit their jobs and move to the countryside?

Well, I don't have a real job to quit, but I can't get fast fiber internet in the countryside, so... hard pass.

"We're fucked," he told me. "Climate change is going to fuck us over. I remember thinking, Should I just accept the deep adaptation paper and move to the Scottish countryside and wait out the apocalypse?"

On the other hand, the Scottish countryside has one thing to recommend it. Well, two things, but mostly: scotch.

But most of all, there's the stark conclusions that it draws about the future. Chiefly, that it's too late to stop climate change from devastating our world—and that "climate-induced societal collapse is now inevitable in the near term."

I knew that without reading academic papers. Well, okay. I didn't "know" that. I suspected that. It's one of the reasons I chose not to have kids.

Look, the time to do anything about climate change was 30 years ago. Maybe even 20. Now? I just don't give a shit anymore.

Back in 2017, even Fox News reported scientists' warnings that the Earth's sixth mass extinction was underway.

Yeah... knowing Fox News, they reported it with a smirk and went on to extol the virtues of tax cuts for the wealthy.

He minces his words even less in his paper: "When I say starvation, destruction, migration, disease, and war, I mean in your own life. With the power down, soon you won't have water coming out of your tap. You will depend on your neighbors for food and some warmth. You will become malnourished. You won't know whether to stay or go. You will fear being violently killed before starving to death."

This is my shocked face:

Climate gloom and doom is nothing new—doomsday preppers have been stockpiling their freeze-dried food rations for decades now.

Fuck that. I wanna be among the first to go. Easier that way. In short:

As an aside, nothing makes me laugh harder than people who hoard gold against the possible collapse of civilization, no matter what the imagined cause. Come the inevitable, gold won't be worth the paper it's printed on; its value depends entirely on how shiny we think it is. "But, Waltz, gold has actual uses! It's a great conductor!" Yeah... that'll be helpful when nothing's generating electricity. No, if you're going to prep, the thing to hoard is coffee. It's not a domestic product in the US, and people are fucking addicted to that shit. Have a stockpile of freeze-dried, tinned, preserved coffee beans or grounds, and you'll be the King, Queen, Grand Nagus, whatever, of the Apocalypse. Possess gold, and people will just laugh. Other options include cigarettes and chocolate. Just be sure you can defend your hoard.

So, like I said, I don't care anymore. I used to. But decades of fighting denial, deflection and outright rejection have taken their toll on me. At this point, I'm just going to ride this sucker down with the hot wind in my hair and a grin on my face.

This is still the most fun slide to oblivion of any civilization, anywhere, and I've decided I'm going to enjoy the whirlwind.

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