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.

January 1, 2022 at 9:14am

#1023961

Airlock.

This year's going to suck no matter what, so why not start it off with rants, courtesy of "JAFBG"

[XGC]?

As usual, I'm just tackling the prompts at random.

Unruly passenger incidents on airplanes have skyrocketed in the past couple years. What do you think about all these in-flight incidents and what should be done about it?

What the hell do you think should be done about it? We live in a world where people are slapped onto a no-fly list for jaywalking, and yet they're not banning all passengers who commit assault in a crowded flying tin can with no survivable escape routes? That is, at a minimum banning them, or for the most egregious cases, they should install airlocks in the tail cone, and anyone who smacks a flight attendant or random fellow passenger gets instantly ejected... whether the plane's still on the ground or not.

If you want to be fair about that last bit, engage the other passengers in a game of Judge, Jury and Executioner, and let them vote on it: Lifetime flight ban, fine, jail time, or airlock; you choose.

Okay, summary execution may not actually fly (pun intended, as always), but a guy can dream, right? How about this, then: Airlines slap a surcharge on everything, already. Extra legroom, checked luggage, bag of ten tiny stale pretzels, oxygen, a toilet visit, whatever. How about for a small fee -- say, $50,000 -- you're entitled to one (1) punch, slap, or kick of a flight attendant. They can still do whatever they want to you afterward, including duct-taping you to the least comfortable seat in Cattle Class, but that one smack'll cost you 50 thousand smackers. Just institute mandatory MMA training for the flight attendants so they learn to take a punch (paid for by the surcharge, of course), and we're golden.

Or, you know, if they're really serious about not wanting passengers to get all unruly and shit, how about not packing us in like sardines? Sure, that'll increase the cost of a plane ticket, thus causing fewer people to fly, but are you concerned about the environment, or not?

Since that's not going to happen, free and mandatory Valium for adult passengers might work, too. Well, not free, obviously, but tack it on as another surcharge because they love doing that. It would be especially fun for us drunks. I was given Valium for (I think) the first time in my life last month, to keep me from screaming in terror as they fucked with my eyeballs, and it worked. Didn't drink afterwards, though.

Vaporized THC in the cabin air is an option as well. No better time to get high than when you're getting high, and stoners don't get violent unless they're also mean drunks or someone laced their weed with PCP or some shit like that.

Speaking of which, I'll also tell you one thing that should not be done about it, but apparently has been, and that's banning drinking or bar services on flights. Shit, alcohol is the only thing that makes cramming into steerage remotely tolerable, and most of us drunks aren't mean drunks; as with everything, the few who are ruin it for everyone else. Or, rather, the pissant airline companies use that excuse to ruin it for everyone else. It's not the poor alcohol's fault; the blame lies squarely on the shoulders of the offending person themself.

In any case, this hardly affects me because I don't fly much these days, for obvious reasons. Sure, there was the Delta flight I took in July when I was stranded in South fracking Dakota, but that was a legitimate emergency. No one got punched, all the flights were on time or early, and no one bitched about having to wear a mask on the completely full planes.

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