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 2 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 4 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.

December 2, 2022 at 12:01am

#1041232

Hoardly Working

I ran into this article a while back, and I figured I'd probably have some things to say about it.

7 Bad Housekeeping Habits You Need to Quit Right Now

I'm guessing one of them isn't "Don't follow random advice from the internet?"

Clutter is just a fact of life. Stuff piles up, messes are made, and dealing with it all becomes one of many things on your to-do list.

There's a difference between mess and clutter. Either way, though, it is true that it is often far easier to acquire something than it is to dispose of it.

Easy enough to manage when life is calm and work is steady, but when things get hectic, it’s more and more tempting to let things slide and deal with them later.

I've been saving stuff for later for decades. I think there are unopened boxes from when I first moved here. I moved here in the nineties.

And eventually, all that procrastinating can turn into what feels like an impossible cleaning challenge.

Or you just decide you can live with the mess. Or the clutter.

And, the best way to regain control is by focusing on and changing your behavior, one bad habit at a time.

I don't have bad habits. I have habits, and if you don't like them, don't visit.

So, read on, and for any behaviors that you know you are guilty of, make an early resolution to start breaking them now — you’ll be surprised how quickly your space will turn around.

I don't do resolutions. And I'm not guilty.

Tossing random items in a “junk drawer”

Drawer? Amateur. I have an entire room for that.

Not cleaning up while you’re cooking

Oh, sure, I'll just wipe that spill off the hot stove burner.

Not treating stains and spots right away

I don't do carpet, either.

Not sorting your mail as it comes in

Oh, come on; doesn't everyone have a stack of mail they'll get to sorting eventually? Sometimes I have to re-stack it if a cat finds it.

Hoarding stacks of magazines you never read

People still read magazines?

Okay, granted, I have subscriptions to exactly two print publications: one for craft beer, which admittedly I rarely read (look, it came with an online subscription thing that I do use); and one for cigars, which I also rarely read, but they like to put glamour photos of hot chicks on the cover. It's just so blatant that I have to admire that publisher.

And yes, I collect the latter. That's different from hoarding.

Putting off laundry until your last pair of socks

I don't wear socks. Laundry gets done when I'm down to my last pair of underwear. That's when I don't say fuck it and order another pack of Calvins from Amazon.

Throwing clothes and accessories on a chair

Oh, bite me. I sit on exactly one chair. The others' sole purpose is to hold my jackets and such. And cats.

...well, okay. That article wasn't nearly as bad as I thought it would be. Usually this sort of article is all about "throw away everything you haven't used in the past week" so that when you do need it you end up buying it again, preferably from one of the publisher's advertisers.

So maybe this will help someone. Me, I'm at the point where changing my habits is more painful than occasionally digging through the junk room for something I just know is in there somewhere.

3 Like • Comment • View 4 comments

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