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!

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

a day 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 29, 2019 at 12:16am

#959811

My Canny Vice

I need help building the stock of prompts in the Challenge War Chest! Write four prompts of your own and then choose one to write your entry on

I get burned out on prompts from judging "Invalid Item"

every week, but I'll give this a shot.

1) If you had to switch places with one other person, who would it be and why? What in particular would you do?

2) Describe your dream vacation.

3) Dogs, cats, both, neither?

4) What one vice do you have that you'd like to quit? Why haven't you?

So, as you might have figured out from the title, I'll pick #4 for myself.

As regular readers know, I have many vices. Hell, I'm probably a one-man vice squad. Fortunately for me, they're all legal. Mostly. Okay, all the ones I'll admit to are legal, and for all you know, that's all of them.

I've come to terms with them, though - one of the few benefits of middle age is that you've either embraced your vices or forsaken them - at some point, my giveashit broke, and the warranty on it had expired.

So, drinking? Check. Smoking? Only cigars, but check. Gambling? Check. Gourmet food? Check, please.

No, the one vice that I'd quit if I could would be my addiction to Coke Zero. I call it Crack Zero. I won't say how much of it I drink, but it's a lot.

I admitted this to my doctor one time, and she shrugged and said, "Well, at least it's not the high-calorie kind." I, of course, took this as a doctor's recommendation to continue.

Now, look, there's a lot of misinformation out there about aspartame and other low-calorie sweeteners. Most of it is bullshit. Some of it is dangerous bullshit, obviously planted by the sugar and/or high fructose corn syrup industry. Aspartame isn't the problem; it's the sodium ions and phosphoric acid and whatnot.

So why don't I just quit?

Short answer: caffeine. Long answer: lots of caffeine. I don't drink coffee; I can't stand the stuff. Never could. I do drink tea, but even the highest-caffeine teas put me to sleep more than they keep me awake - and believe me, I drink some high-octane teas. And while I'm in a position to sleep when I want and wake up when I want, most of the time, without my caffeine I'm just not alert enough to be arsed to do anything.

So it's caffeinated soft drinks for me. Since sugar and HFCS are really, really bad for me (risk of diabetes and all that), I'm left with diet sodas - all of which taste like dysenteric ass except for Diet Dr Pepper and Crack Zero. I'll drink the former if the latter is sold out, which it often is, thanks to me.

Therefore, no, I'm not quitting anytime soon. Ever run into one of those fucking annoying people who are tired all the time, and when you suggest that maybe they get some sleep, they go "I'll sleep when I'm dead?" They think it's some sort of virtue. And you know this means they'll be dead sooner than they otherwise might? It's kind of like that. I'll quit when I'm dead.

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