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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Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

November 29, 2020 at 12:01am

#999320

Promptly

Ah yes, the prompt prompt.

PROMPT November 29th

We need your help filling the Challenge War Chest! In your entry today, write three of your own prompts and then choose one of your own to complete your entry.

1) Talk about a sport or game you like to play. What is it about it that you like?

2) What is the strangest thing you ever saw/experienced?

3) Tell us about the oldest item you own.

And now that those three prompts have popped into my head, ran down my arms and oozed onto my keyboard, I find I don't really want to talk about any of them for myself.

But in the interest of playing along here, I'll use the first one.

Everyone's a nerd about something. It's just that some of us are nerds about nerd stuff. I don't like sports; I like games. Specifically, I like complicated board games and role-playing games.

Here's the thing: I don't much like competitive games, as a rule. Oh, sure, sometimes, but I don't think of them as competitions; I just try to do the best I can at them. I don't like winning because it makes me feel bad, and I don't like losing because it makes me feel bad. I just like playing.

So that's what I like about RPGs: while people can be competitive at times, it's more of a cooperation thing. The idea is how characters of diverse backgrounds can get together and team up to solve problems with combinations of their own unique abilities? That's one of my favorite things. And it's imaginative and subversive, which is why I think there was a lot of pushback to those games at first.

Traditionally, these games required sitting around a table and breathing each other's air, which of course is contraindicated today. But nowadays I've played RPGs with people via online chat; there are platforms specifically designed for this sort of thing. It's not as engaging, perhaps, but it has its advantages. Still, I haven't had the opportunity in over a year, and I kind of miss it. Meanwhile, I'll just have to continue playing video games.

Mini-Contest Results!

Tough choice here. While I'm only awarding one MB, I have decided that everyone who commented yesterday will get a Season Ticket. I'll figure out which one later. I appreciated all of the comments, whether they were in response to the question or not.

Lots of hate for dish-washing yesterday. I can understand that. I hated it a lot before I got a dishwasher. Now it's just annoying to unload the thing. But I'm going to go with one of the bathroom-cleaning ones. Specifically, Cubby's comment successfully disgusted me with its vivid imagery. Good writing, there. So you get today's MB!

I'll do this again soon - won't wait as long this time. So everyone will have another chance.

8 Like • Comment • View 8 comments

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