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').

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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.

May 14, 2021 at 12:09am

#1010154

Universal Plot

Late 30DBC prompt, so I'll edit this later.

Earlier this week was like:

Me: You know... I'm fully vaccinated, more things are open... I could take a road trip, visit some breweries! And maybe some friends! But mostly breweries!

The Universe: *shuts off gas pipeline to most of the eastern US*

Idiots: *hoard gas in plastic bags, further reducing availability*

Me: ...Oh well. Maybe in a couple of weeks.

The Universe: *plots next move against me*

Idiots: *continue to be idiots*

Yes, yes, I know, it's not all about me, and it wasn't the Universe but some cackling Russian hackers. Still, I reserve the right to take it personally.

Edit:

PROMPT May 14th

If animals could talk, which animal would you want to have a conversation with? What would you ask?

Well, certainly not my cats. They talk to me enough as it is, and I don't think I can learn anything new from them being able to say "Feed me, human!" in English instead of Meowese.

Definitely not dogs, either. You know how there are some people who talk a lot, mean well, are very friendly, likeable, and charismatic -- and yet, somehow, never have a single thing of consequence to say? That's dogs.

Absolutely not pigs or cows, either. What am I going to ask them? "So, how do you feel about the wholesale breeding and slaughter of your species for the purpose of delivering unto us delicious [burgers/bacon]?" I mean, I'd rather just go on believing that they're fine with it.

So I'm gonna go with raccoons. You know those little bastards would be great conversationalists, even if you wouldn't be able to believe a single word they said. It'd be like:

Me: So, how was your day?

Trash Panda: Oh, you know, the usual. Watching the birds. Raiding trash cans. You would not believe the food some of you humans waste. Or maybe you would. I mean, I still gotta wash it, but it's definitely edible.

Me: Sounds like you've been busy.

Trash Panda: You have no idea. By the way, while I was rinsing off a particularly ripe apple, I saw a bear coming to eat you, so I chased it away.

Me: A bear?

Trash Panda: Yep. You know. Huge, black fur, sharp teeth, big paws? You're welcome.

Me: ...Thanks?

Trash Panda: So, you know, maybe if I could get your gratitude in the form of a pastrami sandwich? Jewish rye, toasted. Easy on the mustard.

Still, I'm just as glad that animals don't talk. I have enough problems sustaining a conversation with humans.

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