Complex Numbers (Book)

Blog Calendar

◄ July ►
S	M	T	W	T	F	S
	1	2	3	4	5	6
7	8	9	10	11	12	13
14	15	16	17	18	19	20
21	22	23	24	25	26	27
28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Brandiwyn🎶

about 22 hours 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

July 5, 2024 at 8:05am

#1073565

It's Called 'Fiction' For a Reason

It should be well-known by now that one shouldn't get one's facts from comedy sites like Cracked. Especially when that source tells us we shouldn't be getting our facts from movies, either.

5 Universal Beliefs That We Got Thanks to One Single Movie

If you see something in enough movies, you assume it’s true. If every movie has bears growling or frogs ribbiting or vampires hating lemons, we assume that’s how the real world works, because movies are the only form of education we have.

For instance, thanks to movies, I know that cars inevitably explode when run off cliffs.

Sometimes, however, no trend is necessary. All it takes is one influential movie...

Kind of like how the documentary Willy Wonka and the Chocolate Factory taught me how candy gets made.

5 Presidents Are Supposed to Wear Flag Pins

A few years ago, a friend of mine got married. The bride asked me to be her Dude of Honor, so I had to buy a suit. The suit came with a flag lapel pin.

I didn't wear the pin to the wedding. Too political.

You might even say a president wearing a flag pin is redundant, since he’s already the president and his nationality isn’t in question.

Oh, how quickly we forget.

The first president to wear the pin was Richard Nixon, and his staff convinced him to adopt it after watching a 1972 Robert Redford movie called The Candidate.

So, to be clear, the clowns we have in office these days all emulate a disgraced former president, who in turn got the idea from typical Hollywood bullshit.

This explains a lot.

As for Redford, a few years after The Candidate, he starred in All the President's Men, a movie we trust Nixon enjoyed just as much.

Ooooooh, sick burn.

One final amusing note: in the alternate universe of The Watchmen (the original graphic novel, published in the late 80s), the President was Robert Redford. Imagine that, an actor as President.

4 Pirates Used the Pirate Accent

We have this concept of “pirate speak,” of a single accent that pirates use. The more pirate-y the pirate, the closer they’ll adhere to this accent... Our idea of the pirate accent comes entirely from one actor, Robert Newton, and his performance in 1950’s Treasure Island.

Eh, doesn't matter. It's iconic at this point. Arrr. Shiver me timbers.

3 Rabbits Like Carrots

We all associate rabbits with carrots, but the two don’t go together naturally at all. The carrots we eat don’t exist in nature at all, as they’re the result of a whole lot of selective breeding.

Otherwise known as genetic modification.

Rabbit like greens, and they can eat the leafy top of a carrot, but if a rabbit gorges itself on carrots, that’d be like you trying to live on cotton candy.

Or on rabbit meat, for that matter.

Of course, Bugs Bunny wasn't a movie star at the time, but as the article notes, he was emulating Clark Gable.

2 Mohawks Wear Mohawks

The mohawk is a hairstyle. It’s also a name for an indigenous people from the eastern United States, so you probably think that hairstyle is named after the people.

Gosh... Hollywood getting Native American culture wrong. Who could have expected that?

1 Rockets Should Count Down to Takeoff

Except that there's sound reasons for a lot of the countdown. Rockets are somewhat intricate and complicated machines (hence the equating of "rocket scientist" with "genius,") and their launch preparations require a checklist of things to be done in a precise order at precise times. Not that I know anything about it, though; I'm not exactly a rocket surgeon.

NASA got the idea of counting down to launches from a German film called Woman in the Moon. This Fritz Lang silent picture was the first ever big-screen depiction of rocket travel — Georges Méliès’ earlier A Trip to the Moon was a far less serious look at lunar travel.

The Méliès film (itself a Verne adaptation) is the one with the absolutely iconic image of a space capsule getting in the eye

of the Man in the Moon.

Anyway, it's no surprise that NASA got its idea from German cinema instead of French, considering the history of NASA.

Countdowns really are thrilling. Just look at this very article. It could have counted up from one to five, and newcomers to this site may be baffled at why it doesn’t. “Is this a ranking from five to one?” they might ask. It’s not.

Anyone here not expect the self-referential humor? I certainly did.

6 Like • Comment • View 4 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.