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 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.

August 23, 2021 at 12:02am

#1016005

It Was a Dark and Stormy Night

You probably know that the Bulwer Lytton Fiction Contest is held every year, "celebrating" the worst of the worst opening lines. Well, here's this year's.

The Bulwer Lytton Fiction Contest

So fix yourself a Dark & Stormy

(it's that kind of night) and behold the radiance of the tortured prose.

I'll skip the Grand Prize winner; you'll need to go to the link to see that. But here are a few samples.

Despite an exhaustive search, rescuers were unable to locate young Christopher Robin in the Hundred Acre Wood before hypothermia took him, and the animals he once called friends descended upon his corpse like a silly old bear upon a pot of hunny.

-Paul Kollas, Orlando, FL

I mean, come on, that one's so bad it's good.

Dark and stormy, the night screamed like a ravished virgin .... the dark, stormy night ranted madly in a barometric tantrum .... it was an ebonic nocturnal tempest .... the stygian typhoon of eventide .... prosopopeic fuliginous Nyx, enceinte as it were with lachrymal lamia farouche as Hecate, disbosomed upon her terrene demiorb an empyreal borasque.

-Jack Holiday, Burbank, CA

The pitfalls of the thesaurus.

Our story begins in the cozy cottage of Bynnoldh-Dyr, son of Asgwitch-Torgwyr, in the idyllic elven village of Myrthffolwrd, but our book actually begins some two hundred pages earlier, in which you are pummeled by irrelevant history and unpronounceable names, because my publisher is paying me by the word.

-Neil B Harrison, Springville, UT

And this is what happens when you write The Silmarillion before The Hobbit.

Actually, it's fine to do that. Just publish them in the other order.

As the two beheld each other, Lady Asthenia's bosom swelled with love like two perfectly popped pans of Jiffy Pop while Lord Mycort's heart melted like butter, making their union complete.

-Roni Markowitz, Brooklyn, NY

That one made me LOL.

I'm not even pasting the best ones here. Seriously, go look at What Not To Do as a writer (that is, unless you aspire to win this contest). I am, in fact, only going to give you one more, from the "Vile Puns" section:

One time at the hoagie shop the actress Ms. O'Hara asked what the tiny pimiento-stuffed thing in my cheddar-bread sandwich was and I had to respond: "Wee olive in a yellow sub, Maureen."

-Fr. Jerry Kopacek, Elma, IA

Hey! Don't blame me; I'm just the messenger here.

Yeah, after yesterday's slog, this collection is about right. Enjoy!

I went to see Reminiscence on Saturday, but yesterday's blog entry was already too long for me to squeeze in a review.

One-Sentence Movie Review: Reminiscence

Strip the movie of its science fiction, detective, crime, mystery and action elements, and you're left with a story about a guy who really, really should just get over a girl and move on with his life, which he won't because otherwise there's no plot; nevertheless, those genres are blended smoothly together with the romance aspect, and despite its utter lack of anything approaching comedy, it's absolutely worth watching if you're into any of those things.

Rating: 4/5

6 Like • Comment • View 5 comments

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