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:

Write_Mikey_Write!

a day 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

a day 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').

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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.

May 30, 2019 at 12:17am

#959858

Parting Shot

Congratulations on making it to the last day of the competition! What was your favorite prompt from the last month? What was the most rewarding aspect of participating in the competition?

I liked several of them, but probably my favorite prompt was the one about increasing life spans.

As I noted in my response to that one, I'm a science fiction reader and, sometimes, writer, and this sort of thing falls neatly within the realm of science fiction.

This may not ring true to people who aren't as familiar with the genre. After all, isn't science fiction about zipping along at warp speed and blasting aliens out of existence?

Well, yeah, there's some of that, and it can be fun, too. But when science fiction is at its best, it's thoughtful. This has been true from the beginning, when Mary Shelley wrote Frankenstein. She took what was speculative science at the time - the observation that electricity can cause muscle contractions in dead tissue, specifically - and asked the question: what if this means we can reanimate the dead through application of scientific principles; what could the implications of that be?

The fact that the science was a dead end (pun, as always, intended) is irrelevant; what matters is exploring the ramifications. And, from the perspective of literature, providing the right point of view to make it relatable to a reader. The same themes echoed throughout science fiction for the subsequent 200 years. Now, that's influence.

Periodically, we get treated to articles that ask some version of the question: which SF authors of the past got the modern era the most right? While these can be interesting - I think I might have linked to one of them here, a while back - it misses the real point, which is that SF isn't about correctly predicting the future; it's about the intersection of humanity and technology. Anyone can predict the future. Some of them will even get some things right, because probability works that way. A very few of them will get lots of things right. Mostly this is a result of pure chance, not some special insight.

This is why I get all pedantic whenever someone asserts that Star Wars is science fiction. It's not. It's fantasy with science fiction props. Don't get me wrong; I'm a fan - but it would be like calling Fight Club a romance.

Possibly all this is rattling around in my head because I had the privilege of judging April's site contest this month, and the required genre was science fiction. So that got me thinking about it, and about how people perceive it.

So, to get back to the question, I liked that particular prompt because it promoted thinking like a science fiction writer.

What was the most rewarding aspect of participation? Well, for me, as I suspect is the case for many writers, writing something forces me to get my thoughts in order. It reveals flaws in reasoning. It exercises the old neurons. I got some ideas for stories out of it, and reading others' takes on things helps me see what other perspectives might be - another important aspect of writing, else all your characters are just proxies for you. Some of these prompts had me examining things I hadn't given much thought to, which is always a good thing.

So, thanks for the activity, thanks to the organizers for putting it together, and most of all, thank you for reading.

I'll be back soon. This isn't over.

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