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 8 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 11 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 13 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

July 25, 2020 at 12:03am

#989070

Week

What day is it?

Merit Badge Mini-Contest below!

PROMPT July 25th

Reflect on your week. What was challenging? What did you do that made you feel successful? What made you smile?

Reflect on your week.

Time has lost all meaning.

What was challenging?

Keeping alcohol in stock. It keeps disappearing somehow. It's a mystery.

What did you do that made you feel successful?

Woke up in the morning. And again in the afternoon.

What made you smile?

Schadenfreude.

...okay, no, it's not all that bad. I'm well aware of what day of the week it is, and I know exactly why my booze keeps disappearing.

Sunday night, I managed to see the comet. It wasn't all that big a deal, but I had to try, because otherwise I'd never be able to look Phil Plait in the eye again. I wrote about the experience in this week's Comedy newsletter: "Comet Chameleon"

Speaking of the Comedy newsletter, I count getting it completed on Monday morning as a success, though no one saw it until Wednesday.

Getting back to the comet, though, I wasn't in any position to take pictures of it, but a whole lot of other people were. I think I posted a link to APOD here last week, but this site

has awesome photos also.

I have to admit, it's getting harder and harder to deal with being effectively unable to travel. Yes, yes, I know I could go do outdoors shit, but come ON, when do I do outdoors shit? No, the reason to travel, for me, is to drink at bars, stay in hotels, visit breweries, eat at restaurants, gamble in casinos (with money, not health), visit friends, go to Nerd Camp (cancelled this year), and generally be in places where other people are. In other words, I'm effectively unable to travel.

This especially sucks because it's right about now that I would have been leaving on another cross-country trip.

Yes, I know, other people have it way worse than I do. Fortunately, I'm not other people. If I can only kvetch if my situation is the worst possible situation, I'd never kvetch at all, and that's not fun.

But no, it's not "challenging." Just depression-inducing.

Fortunately, yesterday was National Tequila Day, and also fortunately, I had some in my stash.

Key word there is "had." Tenses are fun. In any event, tequila what made me smile most recently.

So, since I'm all down about the traveling thing, or rather the not-traveling thing, I think it's time for another Merit Badge Mini-Contest.

Write in the comments where we'd go if I met you on a trip. I don't know -- maybe thinking about it is a bad idea, but I won't know until I actually think about it. This can be somewhere unique to wherever you are, or some distant location; doesn't matter, since this is all hypothetical anyway (unless you don't want it to be, in which case hit me up when things settle down). Also, no need to limit this to things I talk about all the time; I'm up for new places and experiences. The answer I like best will earn the author a Merit Badge tomorrow.

As usual, deadline is midnight WDC time today (Saturday, July 25).

7 Like • Comment • View 11 comments

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