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').

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 19, 2019 at 12:23am

#966408

Can't Find a Better Man

PROMPT September 19th

Our very own NaNoKit

is getting married today!

Congratulations Kit!

The prompt today comes straight from me:

Write a detailed description of how your significant other (or another loved one) has made you a better person.

First of all,

RUN, KIT! RUN WHILE YOU STILL CAN!

With that out of the way...

Ever notice that it's always "other people" who claim that being a better person means acting less selfishly? In other words, the very people who stand to gain from convincing you that you're better if you consider other people, stand to benefit from you considering other people.

Bit selfish of them, don't you think?

Seriously, though, apart from that, I don't know what qualifies me to be a "better person." Also, I don't have a significant other, or immediate family. I do have friends, of course, and I think they help keep me from egregious errors. My housemate, for example - good friend, but platonic - I'm pretty sure I'd be less diligent about things around the house if I were living alone.

I think about that whenever I get the idea that I want to live alone. I mean, I do want to - never been able to, for one reason or another - but it's probably a bad idea.

Another friend, much younger, keeps me from descending into the quiet chaos of despair. Sometimes it's good for optimists and pessimists to be friends. The optimist (her) keeps the pessimist from giving up completely, and the pessimist (me) keeps the optimist's rose-colored glasses wiped clean of streaks and smudges.

To be specific about one thing we've discussed: I am of the considered opinion that the time to do anything about climate change was about 30 years ago. We didn't do anything, and now it's too late. We're utterly fucked. And I used to care that we're doomed, but I don't anymore. Let the world burn; I won't be around much longer to see the barbecue. Further, at this point, if we did somehow manage to turn things around, the denier brigade would just point at the world and go, "See? Nothing happened. It was all overblown." So yeah, I just want the world to come to a flaming halt so my last words to the deniers could be "WE TOLD YOU SO." And I get these moods where I just want to consume to excess just to help things along.

But having a younger friend makes me want to care, if only for her sake. Not that I do care, but at least I want to, and that's something, I suppose.

I don't consider myself a good person. I mean, I don't kick puppies or treat waitstaff like shit or shoplift or vomit in my Uber rides or anything like that, but that's basic courtesy, nothing to be proud of. So I'm not sure I'd be a worse person without my friends, but I wouldn't care to find out.

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