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 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 30, 2022 at 12:01am

#1042343

Playing Chicken

It's probably shitty of me to rag on this post, but I'm going to do it anyway.

Cold Fighting Chicken Noodle Soup
The most soothing, comforting, cozy soup for the flu season! Quick/easy to make, you’ll be feeling better in no time!

It's the bangs, really. Well, mostly. Everything is just so goddamned exciting! I gotta put exclamation points everywhere!

Happy Monday!

You do know that stuff on the internet tends to be up 7 days a week and, in this case, for over four years, right?

We just got back from San Francisco to watch the Dodgers versus Giants, and we ate so many Gilroy garlic fries and clam chowders in a bread bowl!

At this point, I should have just closed the tab. There is nothing I have in common with these authors.

But as amazing as their food was at AT&T park, San Francisco is also super cold (compared to us weenies with our LA weather), which means I’m now home with one of the worst colds ever.

Article is from the Before Time, when people traveled a lot and happily collected viruses like Beanie Babies.

Also, I have sworn to never visit a stadium, arena, or other venue for which some corporation paid for the naming rights.

I’m currently on bedrest right now with a giant bowl of this soup.

Eating soup in bed, especially while sick (or drunk), takes some serious confidence.

It’s the only thing that is making me feel better at this point. And the garlic/lemon/ginger/lemongrass here is doing absolute wonders.

I have to admit, that does sound like a great flavor combination. Won't cure anything except maybe hunger, but I don't doubt it would provide some comfort and relief.

So as the weather cools down, be sure to stay warm and have this soup on standby! It will be a god-send!

Someone from LA telling the rest of us to stay warm can go fuck themselves.

As for the recipe itself, well... on the plus side, the usual PhD dissertation food bloggers feel the need to write before getting to the goddamned point is mercifully short (I copied most of it above). On the minus side, I count 16 ingredients; 17 if you note that salt and pepper are on the same line.

Worse, I see an awful damn lot of dicing and mincing and grating and chopping and shredding. Way, way, way more work than I want to do when I'm feeling good, let alone when I have a cold. No, as delicious as this soup might be (and it does look tasty), when I'm sick, I can barely muster the energy to nuke a can of Campbell's.

Yesterday, in an ongoing effort to try to do new things, I made a batch stuffed grape leaves. Never done that before. Stuffed grape leaves are fairly labor-intensive and time-consuming, but I had a recipe and I figured, what the hell, right? And they turned out just fine. My only point here being that as complicated as stuffed grape leaves are, it was a simpler recipe that required fewer ingredients than this chicken soup from a site whose motto is "Quick and easy meals for the home cook." (It did take longer, though, I admit.)

And finally, "ditalini pasta?" I've been cooking various forms of pasta for at least forty years, and I've never even heard of that shape, let alone seen it in a grocery store. My spell checker doesn't even recognize it. Maybe y'all in LA can find it on every street corner, but I haven't even seen it in New York or New Jersey, and there are at least a dozen people there of Italian ancestry.

Oh, well. At least I learned something new.

Anyway, no, it's not quick, it's not easy, and it's definitely not an antiviral, but hey, despite all that, and despite the exclamation marks splooged all over the page, it really does look good. If you end up making it, invite me over. As long as you're not sick.

7 Like • Comment • View 3 comments

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