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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 17 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 19 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.

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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