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 13 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 15 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.

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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.

April 9, 2022 at 4:33am

#1030357

Chat? Oh.

Another entry for "Journalistic Intentions"

[18+]...

Chat Piles in Oklahoma

Well, I know what an Oklahoma is (a state containing mostly cows and oil wells); I know what piles are (hemorrhoids); and I know what chat is (French for cat or, alternatively, a casual discussion). But that particular combination of words is nonsense to me, unless "chat" is also Oklahoman for "cow manure." Contrary to popular belief (which I foster), I don't know everything.

I could, of course, follow the link in the JI forum, and probably even learn something from it, but it's way more fun not to. Besides, after being reminded of my Green-Eyed Monster drink creation yesterday, naturally I had to make one in the evening. And then I had to make another one to ensure I got the proportions right. I didn't, so I had to try again. You know... for science. (As a reminder, a Green-Eyed Monster is the result of me looking at a bottle of absinthe and a bottle of Midori and going, "Hmmm..." It's like 1 oz of each, and then add another 1-2 oz of tonic water, over ice. Garnish with, I dunno, some sort of fruit if you want; I don't care.) So my head is pounding way too hard to click on a link and absorb its contents.

And I was about to bitch about Oklahoma's stupid alcohol laws, but just as I was getting ready to do so, a little voice told me, "Waltz... things change; you'd better look this one up." So I did, and behold, Oklahoma's alcohol laws are not nearly as stupid as they used to be, which is remarkable for a state whose constitution, upon creation as a state, reeked of the foul stench of Prohibition. Now, the only foul stenches coming from Oklahoma are the oil wells and cow piles. And maybe the state capitol, but that's no different from any other state.

"Waltz, you won't click on the link, but you went and looked up Oklahoma alcohol laws?" Well, yeah. Priorities, people.

Since I don't live in Oklahoma, and it's usually a state I drive through, not to, it doesn't affect me much, but I always felt for those poor innocent Sooners who were limited to either 3.2 beer, or room temperature beer.

Well, apparently there have been some reforms, so I suppose it's possible there will be more craft breweries there, which I will have to visit, and then maybe I'll find out what chat piles are.

Or, you know, I could go ahead and click on the link in the prompt in the JI forum.

Nah. I'll do it later so I can be embarrassed by this entry.

2 Like • Comment • View 1 comment

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