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 13 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 15 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 13, 2020 at 12:03am

#983432

Dream Vacation

Yeah, yeah, just give me a few minutes to set this up first...

PROMPT May 13th

Writing Sprint! Set a timer for 10 minutes and write without stopping about whatever comes to your mind. I challenge you to deny your urge to edit yourself as you write. If you must, you’re allowed to edit, but only after you finish your ten minute sprint. Ready? Set. GO!

I went for a walk today around the neighborhood.

For, I don't know, six weeks? Seven? I'm starting to understand why some people think time is an illusion. Anyway, for nearly two months, I only left my property to take the trash can and recycling bins to the curb, and replace them the next day. My gym has been closed, and there's nothing else open, and I probably wouldn't go anywhere even if something was open. But I started walking again on Sunday.

It's not -- and a lot of people don't seem to get this -- about me getting sick. I made peace a long time ago, or at least I think I did, with the idea that I could get sick and/or die without warning. No, it's about not getting other people sick, like my housemate who's actively working as an epidemiologist. From home.

Fortunately, I have a decent-sized house and we each have our own area. We get along, and I like to keep it that way. So I've been staying home, and she's been staying home, and we each get groceries delivered. And beer and wine. Still no liquor delivery here, but I have a decent stash. Which of course means that other people get to risk themselves and their friends and family on my behalf. I'd feel bad about it, but it's kind of like, well, I might as well enjoy my privilege while I have it.

Unlike some people, I haven't lost track of the days of the week. Weekends are still weekends. Monday night is Trash To The Curb Night. Thursdays are "Support My Local Brewpub" Day, where I order food and beer (for delivery) from my favorite beer manufacturer. Fridays are my normal days for judging a contest here on WDC. I can tell the other days of the week from those. I only wish the weather would have been warmer. It's May for fuck's sake; we shouldn't have nighttime temperatures dipping into the 30s. Why does this matter when I'm just staying at home? Well, I said I didn't leave my property, not that I don't like to sit on my deck.

But my itch to travel grows stronger. The housemate is looking at buying her own house -- good for her -- so my almost-free cat care when I'm gone won't be around much longer.

--- --- ---

And that's it. I didn't really plan on writing The Covid Diaries, because everyone else is doing it, but what the hell, it's what came to mind. And only minimally edited after the timer went off, so I probably didn't catch everything. At least I was sober for it. What I didn't mention is that, apart from not being able to go to the gym or bars or the cinema, this isn't much different from my life in the Before Times, and I don't expect it to change much when things reopen at some point in the distant future.

But I still want to get back to traveling.

4 Like • Comment • View 10 comments

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