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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 13 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 14 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.

May 24, 2020 at 12:05am

#984212

Rocket Science

It's embarrassing how terrible my memory is for some things.

PROMPT May 24th

Write about something awkward or embarrassing that happened in public - it can be something that happened to you, or something you witnessed happen to somebody else. How did they react?

You know, just yesterday I was taking a nap when I woke up in a cold sweat thinking, "Gosh, I hope the 30DBC doesn't do the whole 'most embarrassing moment' prompt. I really hate those."

Well, this isn't quite that, but it's close enough to make me believe in precognition. Okay, no, not really.

Thing is, I'm sure I've had embarrassing or awkward moments. I must have, right? Everyone does. I have memories of lying awake at night replaying the moments again and again, but I have no memory of the actual moments. Does that make sense? Like, I remember the process by which I edit them out of my memory, but not the actual events because I edited them out.

A memory of such an event can and does pop out eventually, usually right when I don't want it to, and certainly not on demand for prompts like these. After wallowing in the embarrassment, I promptly forget about the event again. Drinking helps.

Similarly, I cringe when something like that happens to someone else. I guess I have some empathy after all, because I don't laugh or bond with other people over how silly the one it happened to is; I just wince and put myself in their place, and then edit it out of my memory.

Even if I could manage to dredge something up, I will have no way of knowing if it was something that actually happened, or something I saw in a movie or TV show.

I could, of course, just make something up, but that would be cheating. Okay, I've made stuff up for these prompts before, but usually only for obvious comedic effect and then I switch to the truth. But in this case, the truth is elusive.

Oh, good, I knew if I typed long enough I'd manage to come up with something. I'm not sure if it's "public," but it happened outdoors and there were people around. When I was a teen, I built and launched model rockets (I still build them sometimes). Some people, kids and parents, came over, for some reason, to witness a launch. Now, the way this is supposed to work, generally, is that the rocket flies up, a parachute ejects, and it floats back to the ground. I'd been talking up how it's safe and fun, and I had I don't know how many people watching when I launched a rocket; it went up, the parachute completely failed to eject, and the rocket buried itself nose-first in the dirt, narrowly missing a human.

Parents herded their children away from me very quickly (an activity I would get used to), and I kept launching rockets. That was probably the only time in my entire rocket science career that an ejection ever failed. Figures it was the one time I was trying to impress people.

6 Like • Comment • View 4 comments

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