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.

November 12, 2019 at 12:04am

#969474

Under Pressure

PROMPT November 12th

What is one thing (sight, smell, sound, object, etc) that, when you encounter it, instantly brings you back to your childhood?

Well, there are these woolly mammoth reconstructions at natural history museums...

Apart from that, there's the barometer.

As I've mentioned before, Dad was a sailor. He'd stopped roaming the seas before I was born, but he had some mementos of his travels, one of which was an old-time mariner's barometer.

It's a simple device, really - a tube with mercury, and a gauge, mounted on wood. It did what it was supposed to do, which was provide a reading of current atmospheric pressure, useful in the times before satellite imagery and official updates as a weather indicator. When I was a kid, it hung on the wall near his antique desk, which I suppose when he obtained it was a new, state-of-the-art writing and organizing surface.

When he died, a lot of the stuff from my childhood home went into storage, awaiting a time when I can either lighten myself of some of these possessions, or find space for them at my house. China cabinets. The desk. Books and a bookshelf. The dining table around which we'd sit in the evenings. Things I don't really have a use, or a place, for, but couldn't bring myself to discard (fuck you, Marie Kondo).

Most likely, I'll keep paying rent on the storage space until I, too, bite the big one.

But the barometer came home with me, and hangs on the wall in a hallway. I pass it several times a day. I can see it, in fact, from my usual workspace.

See, that barometer was probably my first introduction to the world of science, and while I didn't pursue the career of a scientist, it's a reminder to me of our efforts to understand and quantify the vagaries of the inconstant universe in which we find ourselves. And also of the curiosity and objective worldview that he, with some degree of success, attempted to instill in me.

There are other things that take me back to those times long ago, of course - whenever I see Orion looming large in a chill night sky, or gaze upon a wide expanse of still water - but the barometer is a constant presence for me.

Appropriate, I think, given what it measures.

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