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!

a day 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

a day 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.

November 4, 2019 at 12:30am

#968948

Quelle Surprise

PROMPT November 4th

Would you rather be surprised or surprise someone else? Write about it!

Confession time:

I always wanted a surprise party.

I've been to other peoples' surprise parties, even though they never seem all that surprised to me. It's always been on their birthdays, though, so I'd expect it wouldn't have been all that surprising. "Hm, it's my birthday and my friends are all acting weird around me. I bet I'm getting a surprise party!" I never arranged one, because I suck at that sort of thing, so that might explain why no one has ever done it for me.

But that's being pleasantly surprised. Clearly, if it's a negative surprise, I don't want to be the target of that. On the other hand, I'm not a big fan of giving people an unpleasant surprise, either. I mean, I think pranks can be funny if they're played on anyone who is not me, but a prank is one of those things that's funnier in theory than in practice.

With my philosophy of "always expect the worst," I try to avoid getting myself into situations where I'm surprised in a bad way.

I was just thinking today, before I saw the prompt, of all the things that could go wrong if - I mean when - I go to Belgium and/or France. That is, after all, why I'm trying to learn French. Stranded in the Pyrenees (there are worse places to be stranded, I suppose), money stolen, trapped in the Eiffel Tower, that sort of thing. That's why I want to learn French - so I can say "help!" in the local language.

Turns out I've already learned many useful phrases. For example (keeping in mind that some of these might be wrong because, like I said, still learning):

Je veux une bière.
I want a beer.

Je voudrais plus bière, s'il vous plaît.
I would like more beer, please.

Je veux un verre de vin.
I want a glass of wine.

La bouteille de vin pour moi maintenant.
The bottle of wine for me now.

Je dois rentrer à l'hôtel.
I have to go back to the hotel.

J'ai besoin de dormir maintenant.
I need to sleep now.

C'est le matin.
It's morning.

Où sont mes vêtements?!
Where are my clothes?!

So you see, I want to be ready for surprises, even in France.

7 Like • Comment • View 6 comments

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