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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day 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

Nov 14, 2024 at 12:10pm
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

January 29, 2019 at 12:32am

#950674

Cold Hands, Cold Heart

Allow me to share this quote regarding my local weather this week: ”Dangerous wind chills of -45 degrees F (-43 C) to -65 degrees F (-54 C) are expected for most of the period from Tuesday night through Thursday morning. This is a life-threatening situation...” etcetera, etcetera... stay inside... frostbite... etcetera.

My question for you has two parts: What is the worst weather you’ve experienced? And what is your ideal weather?

Allow me to begin by saying that my ideal weather is absolutely not what is described up there.

But... worst weather. I'm not actually sure. I've been in a hurricane, but far enough inland that it wasn't too bad. I've driven through thunderstorms so fierce that I couldn't see past the hood of my car. Once, I crossed New Mexico in a blizzard so outrageously hellish that mere mortals - including state police - had skidded off the interstate and into drifts.

At least they couldn't issue me speeding tickets.

But really, I don't mind extreme weather - hurricanes, tornadoes, whatever, bring it on - as long as it's not fucking cold. Seriously, that shit up there

is straight out of my worst goddamn nightmares. Well, almost worst. Penultimate worst, but bad enough. You know there are places on Mars warmer than that, right? You know that, right???

I despise cold weather. You know I got accepted to MIT, many years ago? You know why I didn't go? Have you ever been to Boston in the winter? Screw that.

Look, I spent my childhood next to an estuary of the Chesapeake, just about at sea level. Pretty close to DC, and you might be aware how crappy the weather can be there. Before I even ventured out of Virginia, I experienced extreme weather: bitter cold, muggy humid heat. And I'm here to tell you that - bugs notwithstanding - give me the heat any day of the week.

Oh, I've heard the argument from frigid people. "You can always put on more clothes, but you can only take off so much." This is nonsense. You don't take off clothes after the heat reaches a certain level; you switch to more appropriate ones, like a loose-fitting black sheet. No wonder you people can't take the heat; you think bare skin is the answer. It is not.

On the other hand, no amount of clothing - no number of layers, no well-made coats or woolen gloves or thermal socks, nothing - will stop my hands and feet from freezing the moment the effective temperature drops below about 52F. And once those freeze, I'm shit-swimming miserable. So you can keep your freakish Michigan lake effect hellish winters (yes, there is a Hell, and it is in Michigan). You can keep your brisk Alaska arctic circle bullshit. You can keep Chicago.

If it weren't for the awesome breweries, wineries, cideries, distilleries, and bars around here, I'd move out in a heartbeat just so as not to deal with another Virginia winter. I've been freezing my ass off most every day since December, and we've only had a few nights of subfreezing lows, this year (last year was relentlessly cold). And I still have February to endure. I don't know how I'll be able to do that. I might just throw my hands up into the frigid air and hop a flight to Maui again.

Because that's where my ideal weather lives.

7 Like • Comment • View 5 comments

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