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!

about 8 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 10 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.

July 12, 2020 at 12:01am

#987883

Blog Standard

I've journaled, on and off, for about as long as I could write.

PROMPT July 12th

When did you first start blogging? (anywhere, not necessarily on WDC) Why? What did you blog about? (subjects, topics, personal news, etc.) Has your blogging style changed since you began?

My first blog began in 2005. It wasn't long after I joined here, and I guess I just wanted to start it on New Year's Day. A resolution of sorts, I suppose, back when I still had some interest in resolutions.

It wasn't this one. Back then the blogs had a lower size limit, and I think I was approaching it, so I created this one instead -- mostly because I thought of the perfect title for it. The old one lasted two years; this one's been around for thirteen, though with a very long hiatus. Never could be arsed to turn off the blog entry notifications in my email, either. Six or seven years of "Your blog misses you! Write an entry!"

Before the first blog, I did things the old-fashioned way: scratches on bark, or cuneiform. Okay, no, it was pen/pencil on lined notebook paper.

My handwriting sucks. Always has. I don't know what happened to those old journals. Hopefully they're smoke now. Later, I started using block caps, which are at least more legible, but the writing was just as pathetic.

As with anything, you get better with practice. At least, I hope I do.

I think I gradually picked up the habit of linking things I found interesting and commenting on them. I mean, for a while there I was all about personal stuff, but my life these days just isn't all that interesting unless I'm traveling -- and I have an offsite blog for that, one that makes it easier to include photos.

It's clear that I gravitate toward certain subjects more than others: various branches of science, philosophy, humor, language, music, drinking, and, yes, writing. I try to stay clear of politics because political arguments make me angsty. Sports is barely even on my radar.

Occasionally I'll look back at my old stuff and go "gods, what an idiot." Chances are that 15 years from now, if I'm still alive and can still see, I'll look back at this entry and go, "gods, what a moron." Chances are even better that a whole bunch of people are already saying that.

Still, because my memory is crap (for anything not involving song lyrics), it's good for me to have a record. And if someone else gets entertainment out of it, too, that's great.

So thanks for reading!

12 Like • Comment • View 12 comments

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