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 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.

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.

July 11, 2021 at 12:02am

#1013434

Just Commit Already

Might as well keep going. "JAFBG"

[XGC]:

No one is perfect. Tell us one thing that your favourite person in the world does that you wish they'd just stop doing.

Can't.

From the forum rules: "Under no circumstances are we condoning bitching, whinging or ranting about fellow WDC members. That shit ain't cool. Don't do it." And the person I'd have to rant about is a WDC member and also reads this blog from time to time. Plus, there's not much to rant about there.

I'll have to settle for someone just a bit lower on the "favourite" (look, I'm keeping the Commonwealth spelling here) scale.

One of the things that bugs me the most about some people is how you make plans with them, and get all your shit together, and psych yourself up to go out into the fiery gaze of the accursed daystar and/or among other people..., and then they go, "You know, maybe another time."

Maybe it's me. Probably it's me. And look, I know that sometimes you just have to cancel. Like earlier this week, I had to cancel a bunch of hotel reservations and other plans for the rest of my trip, but dammit, I had an ironclad excuse. Though blowing me off is still better than an ex-girlfriend I had who was always late. And I mean always. Like, one time, we were twelve hours late for a flight. Twelve. Hours. She wasn't one of those people who did it as a power move, either; she just had no concept whatsoever of time.

No, she wasn't my girlfriend for very long, but we stayed friends. I just knew that I could never count on her to be anywhere on time, ever. One time (I'd married someone else by then) I even baby-sat her kid (by some other schmuck) while she went on a date. "I'll be back by ten," she told me. My mind edited that to "midnight" and planned accordingly. To her credit, she split the difference and got back around 11. By that time, her daughter (12 at the time) and I had gotten into a water balloon battle in her apartment, which pretty much guaranteed I'd never get roped into sitting again. As planned.

But I digress.

So, if, like, say, my other friend and I decide we want to go to Atlantic City (just to name a purely hypothetical, random example), I don't want it endlessly put off until later. Unless, you know, there's a pandemic going on. But absent that, fucking commit already.

Don't get me wrong; this doesn't mean that person isn't my friend, or that we won't eventually go to Atlantic City. We've been friends for a very, very long time, so he's basically a brother to me. Or at least I think so; he had actual brothers, but I didn't, so I don't really know what it's like. But doing anything with him can be like weeding a kudzu garden. To his credit, though, when he says, "hey, let's have lunch around 1," he's there before 1:00. Unlike some people who would show up around 5:30 am the next day.

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