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 2 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 4 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 15, 2023 at 12:02am

#1043148

Revisited: "Meat the Press"

With over 2200 entries here, it's difficult not to duplicate entry titles. Oh, sure, I could do it, but that would involve taking the time to use the search function and possibly slogging through entries with the words in the body in order to see if I've used the title before. And that's work, which, as you know, I'm allergic to.

But it turns out that the title of today's archive post was one I used twice (and now, three times, sort of). in my defense, it's a great pun: "Meat the Press"

.

This one's from not all that long ago—while I exclude anything in the last 12 months from these revisits, this was 15 months ago. I just pick them at random. As noted in that entry, I was participating in "Journalistic Intentions"

[18+], so I'll take the opportunity to plug that contest now. I think the next round will get going next month, and it can be fun to see where the prompts take you. In the case of my linked entry, the JI prompts were all about food; Turkey DrumStik

runs a different theme each time.

As for the entry itself, though, there's not a whole lot I need to add to it.

It's a good thing I'm tackling this now. Today and going into tomorrow, I'll need to be on a liquid diet. And not my usual liquid diet, either. So I expect to be mind-destroyingly hungry, which is never how I want to be when I'm reading or writing about food.

That intro might be confusing taken out of chronological context, so I'll explain: being the age I am, I occasionally get to have a camera shoved up my ass. As a former photographer, I'm used to people wanting to shove a camera up my ass; fortunately, in this case, it wasn't my camera, and I'd be unconscious for it. Point being, apparently, the procedure was scheduled for shortly after that entry, and I was about to start the necessary preparations for the procedure, which involve taking copious laxatives and not eating anything (or drinking beer).

For the record, not that anyone cares, but it turned out that I didn't get all that hungry during the prep, and I got a clean bill of health afterward. You'd never know it, though, the way I overuse semi-colons. (I see an opportunity for a pun and I take it.) I don't remember if I ever followed up to mention that, so I'm doing it now.

Still, it would have been annoying to write about food during a period of fasting.

And that's about all I have to elaborate upon, so read (or re-read) the entry if you want. Unfortunately, the video the prompt is based on is no longer available. It's not required viewing, though. As I recall, it was moderately interesting, although, naturally, not nearly as fascinating as my writing.

2 Like • Comment • View 2 comments

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