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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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.

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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').

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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 26, 2021 at 12:39am

#1010781

Planet Plan-It

Thanks for all the comments and advice yesterday. Navigating the swampland of human interaction can be difficult for me, because I never bothered to buy hip waders, put on insect repellent, or learn which plants will mess me right up. I'd a whole lot rather talk about beer. And even ratherer than that, drink it.

Movie news: It looks like next month is Harrison Ford Month at the Alamo. Blade Runner, Raiders of the Lost Ark, The Fugitive, another Raiders movie... no Star Wars, but that's okay; I'm still sore over The Rise of Skywalker (even The Mandalorian didn't cure me of being sore about TRoS). And as for the new Raiders movie that's supposed to come out next year? Well, to quote Han Solo, I have a bad feeling about this.

Point being, there's plenty of movie opportunities coming up, and that's not counting any new releases. I'm planning to see Raya and the Last Dragon on Thursday, and and some point I'll have to do A Quiet Place II.

Again, I know that many movies don't require going to the theater, especially those classic Harrison Ford movies. I'm going anyway because I like the experience. I can eat at home, too; that doesn't mean I never want to go out to eat. At this theater, I can do both.

Hey look, a wild prompt appeared while I was typing this, so without further ado...

PROMPT May 26th

Make a list of your top five short term goals and a separate list of your top five long term goals. What steps will you take to achieve them?

Short-term Goals:

Let's see... did I mention five movies above? Raiders, Last Crusade, Fugitive, Blade Runner, and (one of these is not like the others) Raya. Yep. That's five.

Okay, that's probably cheating. Let's lump those all under movies.

1) Movies
2) Beer
3) A road trip
4) Fly to Belgium
5) Maybe fly back

1 and 2 are easy to achieve: walk to the drafthouse cinema, spend money. 3 is a little trickier because I need a block of time without commitments here, and that's tough to find in the next few weeks. 4 depends entirely on availability; last I heard, they were planning on letting vaccinated Americans in, but no time frame for that has been set. And if I can't go before the start of September, it'll be next year because -- and I cannot stress this enough -- I utterly despise the cold. Anyway, I'll have a chat with a travel agent who, presumably, knows more of the ins and outs of this sort of thing than the sometimes questionable information found on the internet.

5 is more aspirational. Just saying it'll probably be hard to leave. There's a lot of good beer there.

Long-term Goals:

At my age? HA!

1. Stay alive
2. ... that's about it, really.
3. Okay, travel to other places
4. Maybe write fiction again?
5. Take over the world and make it more fair and just, especially for me.

...yeah, obviously, these are mostly jokes so they don't get a real "what steps" treatment. The fiction writing thing could just as easily be a short-term goal, but I've been so focused on reading / viewing other peoples' fiction that I just haven't been doing my own lately. That's okay; I'm not all that worried about it. For now, doing daily blog entries and two newsletters a month is enough for me.

Really, though -- and you've probably already figured this out about me -- I'm not a very goal-oriented person. This is reflected in my random road trips; there's technically a destination, selected at random, but I give myself as much leeway as possible in getting there. On the road, as in life, for me it's more about the journey than the destination.

And sometimes I think that there is no destination; there is only the journey.

7 Like • Comment • View 6 comments

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