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:

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').

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.

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

1 Like

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

March 14, 2023 at 8:51am

#1046378

Word Origins

Behold, an article related to writing. From Cracked:

Everyday Words And Phrases That Were Invented Onscreen

Writing is inventing, and many everyday words and phrases have come from the magnificent and maddening minds of screenwriters.

And from me, though I haven't managed to convince anyone else of that.

Someone yells “Derp!” and we immediately think BASEketball.

...No. Never saw it.

A person says “red pill” and up pops The Matrix in our noggins as we try not to spontaneously combust.

And there I immediately dismiss anything the person has to say. Not because of The Matrix, but because it's been appropriated by asshats.

Come to think of it, I wonder who came up with "asshat?"

Turns out it's not all that clear

, but the Coen brothers seem to have had a hand in it, or at least a finger, so that's okay.

Now, as usual, this is a countdown list, with 12 items. I'm not going to comment on all of them.

11. ”Catfish”

The 2010 documentary, Catfish, was the first to coin the term describing a person who scams someone by using a fake identity.

Huh. Seems to me it was older than that. Maybe that was just the practice, which is indeed much older than that.

10. ”Gunslinger”

It turns out that no one called those supposed gun-loving sharpshooters of the Wild West “gunslingers.” The term was coined in the 1920 Western movie Drag Harlan, and has become a staple term ever since.

Quick, someone alert Stephen King. Also, don't bother with the movie.

7. ”Google”

Thank Buffy the Vampire Slayer for being so tech savvy and turning “google” into a verb. The moment happened in the 2002 episode, “Selfless,” in which Willow asks Buffy: “Have you googled her yet?”

Almost every company wants their brand name to become generic. Like Kleenex or Band-Aid, or Coke. Unless, of course, it's pernicious, in which case, lawyers get involved.

5. ”Nimrod”

Another word that was already in existence — its original definition means “skilled hunter” — but was changed in meaning thanks to Daffy Duck from Looney Tunes fame who used it to insult hunter Elmer Fudd, implying that Fudd's “a buffoon.”

This one, I knew. Nimrod is from the Bible. I like Looney Tunes' take on it better.

3. ”Friend Zone”

Written as part of Joey Tribbiani’s dialogue in “The Blackout” episode of Friends, the phrase took a while to catch on and, perhaps, would've been lost in the ether … if it weren’t for every second online publication writing a puff piece about the dreaded and, let’s face it, entitled concept of being “friend zoned.”

Pretty sure I remember that from before, too. But I could be wrong. Also, I never saw a single episode of Friends; it was on during the time I swore off (and at) television.

There's lots more at the link. Words have power, and if you can come up with one that sticks, well, that's really fetch.

4 Like • Comment • View 2 comments

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