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!

about 19 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 21 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.

February 6, 2020 at 3:09am

#974958

Come the Revolution...

For various reasons, I decided to get completely drunk yesterday. Then I came home and passed out; hence the relatively late entry today.

https://www.fastcompany.com/40467032/the-end-of-capitalism-is-already-starting-i...

The End Of Capitalism Is Already Starting–If You Know Where To Look
One of America’s foremost Marxist economists has never felt so optimistic in his 50-year career.

Americans like to think everything is binary. You're either an alcoholic or a teetotaler. Anyone who's not vegan is a murderer. If you're not a Republican conservative, you're a liberal Democrat. That sort of thing. But reality isn't binary; it's spectrum - so the choice isn't "capitalism" or "socialism" but any number of in-betweens.

Over the summer, inequality experts Jason Hickel and Martin Kirk launched a conversation on this site when they posed the theory that capitalism is at the core of the many crises gripping our world today.

Actually the core of the many crises gripping our world is that there's too many people on it. But every time someone points that out, someone else goes, "So go ahead and kill yourself, then." If enough people urge me to do so, I probably will, so I'm not going to dwell on the too-many-people hypothesis.

“Americans are getting closer and closer to understanding that they live in an economic system that is not working for them, and will not work for their kids,” Wolff says. Growing awareness that wages have been unable to keep up with inflated costs of living have left younger generations particularly disillusioned with capitalism’s ability to support their livelihoods, Wolff says, and with CEOs out-earning employees by sometimes as much as 800 to 1, it makes sense that public interest should be swinging toward a workplace model that encapsulates shared ownership, consensus-based decision making, and democratized wages.

Which is one reason I didn't have kids.

Also, I mean, that has been completely obvious to me for a long time, so obvious that it went without saying: instead of "management" and "unions," why not have workers with a stake in the company? Again, non-binary.

“The image of the transition from feudalism to capitalism was the French Revolution, and that was part of it,” Wolff says, “but it wasn’t the whole story. The actual transition was much slower, and not cataclysmic, and found in these serfs that ran away and set up something new.”

A friend of mine is fond of sending me gifs of guillotines whenever some super-rich capitalist shithead does something to fuck the rest of us over. While I owe my existence and all of my luxuries and luck in life to capitalism, I can't say I disagree.

Anyway, I didn't link this article because I agree or disagree with it; again, life isn't binary, and I don't feel the need to fling myself to one side or the other. As with science, I just find it fascinating and worth watching. It's something to think about, especially if you're trying to find a decent job and health insurance in today's "booming" economy.

3 Like • Comment • View 2 comments

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