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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Brandiwyn🎶

a day ago
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').

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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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

December 1, 2020 at 12:55am

#999441

Do I Dare To Eat An Apple?

I don't usually participate in the 30DBC Unofficial Months. If you've been following me for a while, you might recall I tried at one point but it just wasn't working for me. But this month seems to have a bit of a different format, so let's give this a shot. This could be fun.

1. Today is Eat A Red Apple Day.
Your entry should be inspired by red apples.

So here are some facts about apples:

1. "Apple" was originally a generic word for "fruit." The French equivalent word, "pomme," was also a generic word for fruit, hence "pomme de terre" for potato ("fruit of the ground") and "pomegranate" ("fruit that's as hard as a fucking rock").

2. Apple, Inc, formerly Apple Computers, formerly "that thing Steve's cluttering the garage with can you ask him to move his stuff?" wasn't named after the fruit but after the Beatles' record company of the same name. Hence one of the early Apple computer's names, the Macintosh, which is named after a common raincoat from Liverpool.

3. An apple invented gravity. It is not known whether this apple was red or green, but at relativistic velocities it doesn't matter.

4. Johnny Appleseed is credited with introducing apples into North America, where they became an invasive species and had to be eradicated by planting kudzu.

5. Contrary to popular belief, it was not an apple that Eve ate, but rather a banana. When Adam saw this, he got Ideas and God got Angry.

6. The botanical binomial of the commonly cultivated apple tree is Malus Domestica, which four years of Latin classes taught me means "Bad Servant." Apparently nobles used to throw apples at their peons who were misbehaving.

7. When an apple is cut up for making apple pie, it generally loses its a-peel.

8. New York City is called the Big Apple because Dutch merchants traded a big apple for Manhattan Island. Later, the English took it over and corrected the spelling from "Appel."

9. Red apples get their coloration from the blood of the sacrifice victim buried under the tree's roots.

10. It's said that "an apple a day keeps the doctor away." I don't know how true this is, but I keep a few by the door to fend off roving bands of surgeons.

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