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 9 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 11 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.

February 14, 2022 at 12:02am

#1026662

Literately

As a reminder, I'm traveling most of this week, so updates may be at irregular times.

Since I still have to pack, this one will be blessedly short.

Poe Boy
The ongoing impact of Edgar Allan Poe

Article is from last October, which is when people actually remember that Poe existed, but anything about him is always timely as far as I'm concerned.

In the early hours of January 19, a shadowy figure glides into the Westminster Hall and Burying Ground through a side-gate and makes his way to a cenotaph. In the biting Baltimore night, the black-clad stranger — in wide-brimmed hat and a long scarf obscuring his face — stands staring at the raven engraved upon the cenotaph. He pours himself a glass of cognac and raises a toast. He bends down, places three roses and the unfinished bottle by the monument, and wafts softly away into the fog.

And already I'm getting a headache. The Poe Toaster (or, if you will, Poester -- okay, you won't, and neither will I) is a wonderful story, but I thought we were going to talk about actual Poe.

To be fair, the rest of the article does get to the point, or points, if circuitously and with precious prose unbecoming of a tribute to Edgar's own style. Poe famously traipsed all up and down the East Coast, and lots of cities claim him: Boston, where he was born; Baltimore, where he died; Richmond, where the oldest extant building in the city is now a Poe museum; Philadelphia, for reasons expressed in the article. And less than two miles from my house is the dorm room where he briefly lived while attending the University of Virginia, so we get a claim on him as well.

But he really belongs to everyone, and to no one.

Anyway, I won't quote more from the article, partly because it's all hooked together in typical epi-pseudo-post-après-modernist (or whatever they're calling the style these days) fashion (I can't resist the temptation to coin Poe-modernist), and partly because despite my personal grievances with the writing style, it's still worth reading.

And though I brought this article up at random, I find it darkly appropriate that it happened to arrive on Valentine's Day.

For the moon never beams, without bringing me dreams
Of the beautiful Annabel Lee;
And the stars never rise, but I feel the bright eyes
Of the beautiful Annabel Lee;
And so, all the night-tide, I lie down by the side
Of my darling—my darling—my life and my bride,
In her sepulchre there by the sea,
In her tomb by the sounding sea.

4 Like • Comment • View 1 comment

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