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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🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Snowman Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

January 10, 2009 at 1:47am

#628842

Civilization

The word "civilization" can be interpreted as "the art of living in cities."

The hotel I'm overnighting in doesn't have a fourth floor.

The elevator numbers go from SC (sub-cellar) to C to L to 2, then 3, then 5-9. I'm on the ninth floor. I'll call it the penthouse suite although it's about the size of my bedroom at home (which is to say: the size of the closet in many modern homes).

The hotel is in downtown Flushing, which is in Queens, which is in New York City. Nearby are the grounds where two World's Fairs were held - one significantly more famous than the other.

One of the great paradoxes of a city is how cramped everything is, and yet they leave room (at least, here) for wide, open spaces - after all, we've been evolving for billions of years (yes, billions; I hope I've scared all the young-earth creationists away from this blog by now) and have only had "civilization" for a paltry few thousand. I guess we haven't quite perfected the art.

The dominant local culture is of Chinese origin. Most of the shops are signed in what I assume to be Chinese characters. This hotel boasts multilingual hospitality: English, Chinese, Spanish, a few others; it appears to be owned and run by ethnic Chinese.

Perhaps there's a cultural aversion to the number four, just as many high-rises built by European-Americans skip the 13th floor. I wanted to ask at the desk about it, but didn't want to be rude or seem like a Bad American. Bad enough I wasn't thinking and put on my Serenity t-shirt for the trip - has what I sincerely hope is the actual Chinese ideograph meaning "Serenity" on it, and not "I am a Bad American."

The drink machine doesn't chill properly, and I ended up with a warm Sprite. I'm pretty sure that's a maintenance fault and not a cultural superstition.

I spent a few minutes walking around the center of town. You hear stories about how dangerous it is in a city, but who's going to fuck with a big guy in a trench coat? Nice place. Interesting shops. Starbuck's on one corner; I didn't go in.

Tomorrow - that is, later today, after I get some sleep - I'll go see my aunt. But I'm only here for one night; the only train I could catch going home leaves at 3am on Sunday morning. Turns out UVA classes restart on Monday, which explains why everything else was booked. I'll be spending tomorrow night in Penn Station and in transit.

Long weekend. Probably won't be back on until Sunday evening.

(Edited to add: after I wrote this I did remember something involving the number four in some Asian cultures and finally hit on the right Google search to confirm it. Apparently, the word for "four" is very similar to the word for "death" in at least China, and so there's a cultural aversion to it. Makes me wonder why they don't just come up with a different word for "four," but I suppose it'd be kind of difficult selling it to the over one billion speakers of some dialect of Chinese.)

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