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 11 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 13 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.

June 21, 2020 at 12:10am

#986107

Business

Entry #6 for "Journalistic Intentions"

[18+]

3. That's always an interesting concept when you try to mind your own fucking business then you end up on face book or twitter.
plainsue

So, again, no idea what the original quote was, and it probably doesn't matter.

If you've been following along, you already know I'm no fan of social media. This site here is about the closest thing I ever use to social media, because it's relevant to my interests and most of us at least try to be kind to each other, or, at least, not hateful. There are exceptions, of course, and being a mod probably skews my viewpoint, but by and large I've had much better interactions here than on Facebook.

I haven't used my Facebook account in years. Every time I think, "I should close that account," I realize I have no idea what the password is. And then to recover the password, it makes me identify friends from their pictures.

Difficulty #1: Most of my Facebook friends are from this site, and I haven't met most of them in person.

Difficulty #2: I have mild face-blindness, so I can't identify faces even of people I know most of the time.

So, yeah, if you've tried to get in touch with me on Facebook, or friend me there, I'm not ignoring you. I just can't log in or close my account.

Apparently, Facebook is forever.

Twutter's another story. I first heard of it, I don't know, sometime back in the noughties before it became the Official Platform of the Pronouncements of the Most Powerful Person in the World. The way I first heard of it, a friend of my then-wife was talking about it. She's an engineer with a rather earthy sense of humor, and she described with some glee how a fellow engineer had rigged his office chair to Twit every time he farted.

As far as I've been able to determine, that site hasn't improved any since then, and may have even gone downhill. Considering that I think fart jokes are the lowest form of humor, that's really quite a feat.

So, no, I don't have a Twatter account and never have. The occasional really interesting thing from it always gets posted elsewhere, so I really don't feel like I'm missing anything.

And don't even get me started on the cesspool that is Instagram. Fortunately, that's not part of the quote above, though as it's owned by Facebook, it's relevant to mention it.

Oddly enough, I've made a shit-ton of money from Facebook. But that's another story entirely.

I've heard people say that the internet is not reality. I don't think that's the case. I was an early adopter, back in the nineties before everything turned commercial, and even then it was an extension of reality. I've met people from all over the world, first online and then in person. Some of my closest friends became so on this site, before I ever met them in person. To say that it's not "real" is to dismiss the people on the other end of the network as non-people, and I think it's dangerous to label anyone as a non-person. That never ends well.

So I understand the draw of social media. I just don't participate. I'd rather mind my own business, and if some picture of me ends up on social media, well, I just shrug and go on with life. But then, I haven't done anything egregious enough to get doxxed or called out. If I did, though, it's probably a sign that I'm not actually minding my own business.

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