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.

November 30, 2019 at 12:20am

#970710

I Felt So Symbolic Yesterday

PROMPT November 30th

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

Well, that was a fast 30 days.

I am shocked to report that my favorite prompt was the Thanksgiving one. You remember, the five-sentences one? I didn't expect that one to be my favorite. No, not at all. I went back to my hotel room on Wednesday, having achieved beerenity, and read the prompt and was like, "But there's nothing I'm going to enjoy about Thanksgiving."

And then the next day I saw that damn rainbow and I nodded and I was like, "Okay. Okay, Universe. Fine. You win this round."

But hey, to be fair, the rest of the day wasn't bad. It's just that it had a high bar to clear after that.

Today, though... you know, some days just work out. Er... by "today," I mean of course yesterday, because I'm posting this at my usual first-hour time on Saturday, but since I haven't slept I still consider it to be today. But it was yesterday. Time is relative; shut up.

Point is, today I saw Bob Dylan on stage. Whatever you think of his music - honestly it's not my favorite, either - there's something special about being in the same room with someone who redefined an entire art form.

But even before that, as I was pre-loading at a taphouse - I did say in a blog entry earlier this month that I wanted to drink more before the end of the year, and, well, mission fucking accomplished - I had just achieved beerenity when this song played over the place's speakers:

Which is Counting Crows' homage to Bob Dylan.

Mr Jones and me
Stumbling through the Barrio
Yeah, we stare at the beautiful women
She's perfect for you
Man, there's got to be somebody for me
I wanna be Bob Dylan
Mr Jones wishes he was someone just a little more funky
When everybody love you
Oh! Son, that's just about as funky as you can be

Seems like the surefire way to make me feel actual happiness is beer and music. Especially if there's something meaningful about the music. There is, of course, always something meaningful about beer.

So. Anyway. Fellow 30DBCers, thanks for reading and commenting - really appreciated all the comments, also enjoyed reading your blogs. Hope you'll stick around; I'm not going to stop posting, though I can't say I'll hit every day in December because I have more traveling (and drinking) to do. Until then, rock on!

9 Like • Comment • View 11 comments

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