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 29, 2019 at 10:34am

#970677

You're A Mean One

PROMPT November 29th

Write about gifting! What’s on your list? What do you have your eye on for yourself and what do you want to gift to your family and friends? Homemade or store bought? What was the best gift you ever received?

Yay! An opportunity for me to Grinch out!

Here's the thing about gifting: it's an unnecessary verbing of a word when there's a perfectly good verb form already available.

Here's the thing about giving: I'm weary of it.

Oh, sure, it was fun to get presents when I was a kid, just like with everyone. But now that I'm ancient, and already have enough stuff, it just takes up space. I feel terrible about throwing it out (honestly, I feel terrible about throwing anything out, because even if it wasn't given to me then I remember the joy of the acquisition of it). Look, if there's something that I want that I can afford, I just buy it. If there's something that I want that I can't afford, nobody who is likely to buy me a present can afford it either. Between Amazon, Uber Eats, Instacart and other services, I can have anything I want delivered to my door in a week or less - usually 24 hours or less. Sometimes even half an hour. I want a movie? Instant. Music? On demand. A game? Almost instant download. I truly live in a utopia.

Well, a utopia for me, anyway. The peasants doing the manufacturing, packaging, sorting and delivery might not see it that way, so I'm always on the lookout for signs that La Révolution is finally here

But I digress. Yes, I do take some joy in giving gifts. But I'm absolutely terrible at matching a gift to the recipient. And then I get worried that they'll think that this is because I don't care enough. "How can he not care enough? Am I wrong about us being friends? Maybe I'll just back off." And since I've had a lot of friends go away, I can't help but think that it might be at least partially because I can't figure out a good present for them. Partly I know it's because I'm an antisocial asshole, but the gift thing causes me tremendous anxiety is what I'm saying. And probably contributes to the antisocial thing.

Handmade gifts are nice, but they, too, make me feel bad because I have absolutely no creative talent whatsoever, so I can never, will never be able to reciprocate.

So yeah, what I'm saying is: I have mixed feelings about gifts. I always appreciate the effort. Always. Even if I get a rock. And I try to make the effort, myself; it just always makes me feel inadequate.

That said, if anyone wants to give me GPs or money, I promise not to feel bad about it. Just saying. That's the best gift I ever received: money. It's so useful for so many things, it takes up hardly any space, and hopefully it's not handmade.

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