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:

Elycia Lee ☮

about 5 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 21 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 23 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

March 23, 2020 at 12:01am

#978883

In The Neighborhood

I found this interesting because it's a kind of insight into the writing process. It's from a couple of years ago, but whatever.

https://www.theatlantic.com/family/archive/2018/06/mr-rogers-neighborhood-talkin...

Mister Rogers Had a Simple Set of Rules for Talking to Children
The TV legend possessed an extraordinary understanding of how kids make sense of language.

And, yeah, it's kind of a plug for a book, but again: whatever.

For the millions of adults who grew up watching him on public television, Fred Rogers represents the most important human values: respect, compassion, kindness, integrity, humility.

And cardigans.

He insisted that every word, whether spoken by a person or a puppet, be scrutinized closely, because he knew that children—the preschool-age boys and girls who made up the core of his audience—tend to hear things literally.

This is something I think every writer needs to keep in mind: not the talking-to-children part, unless that's your goal, but the necessity of knowing your audience. Or as a comedian might put it, "Read the room." Only for a writer, the room is the world, or at least a part of it.

For instance, Greenwald mentioned a scene in a hospital in which a nurse inflating a blood-pressure cuff originally said, “I’m going to blow this up.” Greenwald recalls: “Fred made us redub the line, saying, ‘I’m going to puff this up with some air,’ because ‘blow it up’ might sound like there’s an explosion, and he didn’t want the kids to cover their ears and miss what would happen next.”

You know, ordinarily I'd say that demands like that would be enough by themselves to raise peoples' blood pressure, but I choose to believe that Fred Rogers knew how to speak kindly to adults, too.

And Rogers’s secretary, Elaine Lynch, remembered how, when one script referred to putting a pet “to sleep,” he excised it for fear that children would be worried about the idea of falling asleep themselves.

I'd think that pet euthanasia, or really death in general, would be a difficult topic to work into any kids' programming (though I'd certainly have fun with it in a parody aimed at adults). But if anyone could do it, Rogers could. Of course, I grew up with that show, but I don't remember too many specific scenes; certainly none involving dead puppies.

Rogers also wrote a song called “You Can Never Go Down the Drain,” because he knew that drains were something that, to kids, seemed to exist solely to suck things down.

Oh, man, I wanna have so much fun with that. "You Can Never Go Down the Drain, But Your Soul Can."

In 1977, about a decade into the show’s run, Arthur Greenwald and another writer named Barry Head cracked open a bottle of scotch while on a break, and coined the term Freddish. They later created an illustrated manual called “Let’s Talk About Freddish,” a loving parody of the demanding process of getting all the words just right for Rogers.

Can you say "scotch," boys and girls? Scotch is a fountain of creativity. Do you know what creativity is? It's what happens when you drink a lot of scotch. Ask your parents where they keep their scotch.

This is one of the reasons Rogers was so particular about the writing on his show. “I spent hours talking with Fred and taking notes,” says Greenwald, “then hours talking with Margaret McFarland before I went off and wrote the scripts. Then Fred made them better.” As simple as Mister Rogers’ Neighborhood looked and sounded, every detail in it was the product of a tremendously careful, academically informed process.

Getting back to being serious for a moment... again, I think this is important for all writers. Well, not this specifically, but the general idea - editing, researching, being aware of your audience, and knowing what you're writing.

But mostly what's important is scotch.

3 Like • Comment • View 2 comments

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