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').

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.

July 14, 2021 at 12:02am

#1013599

Rant Mode On

And another one for "JAFBG"

[XGC].

Tell us about something/someone that fucked you off this week.

Well. If we're only going back a week, I could talk about the rental car company, who overcharged me. Okay, they didn't really; it cost exactly what it said on the label. It's just that there were only two rental companies in town. You know them; they're the big names: Hertz, named after the electric shock you get when you see the bill, and Avis, which is French for "opinion" as in "in my opinion, Hertz sucks balls, but Avis is worse."

So, with no competition, they can charge whatever the hell they want to charge. And why is it that they make you bring the car back with a full tank of gas, forcing you to buy gas from the nearest station to the car lot, which inevitably has a 25% surcharge on fuel? Which is still better than the $6 a gallon they charge if you fail to fill the tank, but it's still robbery.

I rented the car on Monday but returned it Wednesday morning, so it's still technically less than 7 days ago as I write this.

Also on Wednesday, I flew home. Delta. Oh, I would love to rant about Delta... but the flights weren't all that bad, considering, and in a stark reversal from its usual policy, the Universe didn't hit me with a bunch of delays and cancellations that usually force me to find alternative means of transportation.

Still, airplane food, amirite? If only they still served booze on the flight. Makes me want to swear off flying forever, but there's no other way to get to Belgium next year.

Or I could complain about that perennial goblin, the DMV. Or BMV in some states, but here in Virginia it's the DMV. You all know the drill: in normal times, it's long lines and crowded waiting rooms. Bringing a copy of War & Peace won't cut it; you gotta bring the entire Wheel of Time series. Or, at least, that's what it would be if they still let people just wander in.

Let me back up. Because my car was totaled, I need to give the insurance company my title to the thing. Naturally, it's... somewhere. Who knows? So I need to get a replacement title. As such, I have two choices:

1) Make an appointment for seeing the one remaining employee at the DMV -- currently, there's nothing within 90 days, and they only schedule within 90 days. Or

2) Fill out a form online and wait up to 15 business days for them to mail me the replacement title.

Obviously, option 2 is marginally faster. Or would be if their website worked. Okay, to be fair, it probably works fine, but only if I turn off all the tracking prevention add-ons I have to slap onto my browser in order to have some measure of security.

If I don't find the title somewhere in my house today, probably under a pile of useless garbage, I'll try the online form with a different browser. As long as I only visit the DMV site, there's not much they can track, right?

But let's face it, the DMV is a too-easy target for rants.

How about my discovery that every car available right now for purchase, of which there are few, is overpriced?

I mean, this is not really a discovery. Supply chain issues, especially regarding computer chips, are well-documented. I knew this going in, but then, I wasn't expecting to have to replace my car this year so I figured, wait a couple more years and this shit will get sorted out. Well, I can go without a car for a while -- there was a period of six months last year when I didn't drive at all -- but eventually I'm going to have to suck it up and buy something.

But really, despite all this, I've had a pretty good week. I get groceries and beer delivered, and almost everything else I need is in walking distance. Which would be good for me if temperatures weren't in the 90s, but whatever; it's July in Virginia, and that shit happens, climate change or no climate change.

So, yeah, prompt or not, I don't mean to give the impression that life is some sort of slog. It's not. It's just that I can find something good and something bad in any given week, and for this prompt I kind of had to dredge something up.

8 Like • Comment • View 8 comments

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