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 3 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 5 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.

September 30, 2020 at 12:02am

#994640

When September Ends

Ah, yes, the traditional end to a 30DBC month.

PROMPT September 30th

Congratulations on making it to the last day of the competition! What was your favorite prompt from the last month? What was the most rewarding aspect of participating in the competition? Did you learn anything about yourself or your fellow bloggers?

Do I even have a favorite prompt? Unlike some previous months, I enjoyed writing to most of these prompts. I only recall one or two which presented issues for me, like the bit about spare time. I suppose I'll pick the "favorite seasonal thing" prompt from a few days ago, because it prompted me to write about one of my favorite subjects: beer.

The most rewarding aspect, and I don't remember exactly how I've responded to this question before but I suspect I'm going to be repeating myself here, is seeing the variety of other peoples' responses to the same prompts. We're all coming from a different place, so we all have our own takes on things. While it's nice to find people who agree with me, it helps me grow and think when someone has an entirely different worldview.

Did I learn anything? Sure. I always learn something. Sometimes I forget it immediately; at this point I need repetition to drill something into my head. I know I didn't comment on every entry I read, and I didn't read every entry, but the ones I saw demonstrated thoughtfulness and care in their answers -- whereas I'm aware I'm often sarcastic and sometimes prefer to inspire laughter than delve deep into the philosophy of some prompts. But that's okay, as far as I'm concerned. So I guess that's what I learned about myself, or, rather, confirmed: that I like being the comedian.

I suppose I should try for even more comedy, but you know, sometimes I just want to be serious. This may confuse people, though, and make them think that I'm trying to be funny when I'm not. But that's not nearly as bad as not being funny when I'm trying to be. That shit's downright embarrassing, like when you drop your pants for sex and the woman points and giggles. Or is that just me? Probably just me.

Anyway, I expect to be around next month too, just doing different things. Maybe I'll attempt some 30DBC Unofficial Month prompts. Almost certainly I'll take a stab at "Journalistic Intentions"

[18+]. Probably it'll mostly be me riffing off of interesting (or stupid) articles that are lurking in my Blog Fodder folder.

Oh, and I'll resume handing out Merit Badges in mini-contests. After spraying out a bunch of them early this month, it's been a few weeks again, so be on the lookout for those.

Anyway, it's been a good blogging month -- thanks to all of you for reading, commenting, and running the 30DBC. See you tomorrow!

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