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:

Wordsmitty ✍️

about 11 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 14 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 16 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

Lilli Munster 🧿 ☕ 🎃

Sep 24, 2024 at 9:10am
In response to "All Out of Louvre"

Have a wonderful time in France. Have you run into Annette in France yet? She's there too!

2 Like

June 5, 2020 at 12:01am

#985027

Oh Behave

Here's another entry for "Journalistic Intentions"

[18+].

2. Well-behaved women rarely do behave well, they just make everyone else think they do.
catty

I'm familiar with the original version of this. "Well behaved women seldom make history." Fair enough, I suppose, though I'd argue that well-behaved men seldom make history, either, making that a nonsequitur of sorts.

There's more than one way to make history, and just because you do doesn't mean you've done a good thing. Carrie Nation, for example. Certainly not well-behaved, and one of the most evil people who ever existed.

But this isn't about the original quote; it's about the remix.

We all have our rebellions. Nobody does everything expected of them, all the time. Not only is that impossible, but if you told me you never even once rebelled as a teenager, you're either lying or boring. Hell, most of us make it a point of pride. "I was supposed to go to work today, but I called in sick. Yeah, sick of work." The important thing in a situation like that one is to not brag about it on social media.

In fact, so many people have been busted for doing something naughty because they posted about it on social media that I have had to once again lower my opinion of humans' collective average IQ.

Of course, there's misbehavior and then there's outright fraud. I have no sympathy for someone who claims disability for a bad back and then posts pictures of themselves climbing a mountain in their copious free time, and thence gets their benefits cut off. But stuff that's not really hurting anyone? Eh, you do you, or whatever the saying is these days.

So if I ever see someone, of any gender, who presents themselves as a fine, upstanding member of society, always doing the Right Thing, signalling the fuck out of their virtue, well, I don't buy it. Oh, I'm sure that, like I said, there's a preponderance of good people in the world, but also like I said, sometimes good people do naughty things. If you're vegan, I assume you sneak a bite of cheese every now and then. If you're always talking about recycling, I bet that sometimes you get in a hurry and throw an aluminum can into the landfill trash. It's okay. I don't think less of you for it. I don't even think less of you for lying about it, because really, you're not hurting anyone and a little bit of rebellion can feel so damn good.

But if you're a fiery anti-sex preacher and you get caught having an affair? Then I'm going to laugh. Or you pull a Carrie Nation and rail about the evils of alcohol, and I find you getting wasted in a bar 100 miles from home? You're damn right I'm going to take pictures and spread them around.

We're all hypocrites to some degree; no one can be perfectly consistent, especially over time and growth. But if you're going to be that blatant about it, you will definitely get called out.

And no, I'm not going to take the gender bait. Not this time, anyway. I reserve the right to be hypocritical about that in the future.

3 Like • Comment • View 2 comments

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