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:

Allan Charles 🐾

about 3 hours ago
In response to "Revisited: "Forgive Me, For I Have Zinned""

I find White Zinfandel to be disgusting. Defining it as the wine equivalent to American cheese is a great comparison.

At my job, we only sold a cheap house wine for white zin, and when people ordered it I had to try to restrain my facial muscles from giving stank face.

1 Like

tj wanderlust-words-in-motion

about 19 hours ago
In response to "Apparatus"

And then we have "cocktail" which can, if one takes the time to look it up, waste a good hour or more of time and provide various meanings and origins, including shoving ginger up a horses arse!

tj wanderlust-words-in-motion

a day ago
In response to "Thwip"

Put it on ATVs so when they get stuck they can shoot out a web and winch themselves out.

2 Like

tj wanderlust-words-in-motion

Feb 20, 2025 at 6:10pm
In response to "One Fine Thing"

Well, it was a fine idea.

Adhere - Definitely Writing

Feb 20, 2025 at 7:48am
In response to "One Fine Thing"

I immediately thought of "Imfamy, imfamy, they've all got it imfamy." But then my mind does that.

2 Like

tj wanderlust-words-in-motion

Feb 19, 2025 at 3:59pm
In response to "Fail to Succeed"

In one way, it's good to have people with boneheaded ideas, it provides something to blog about.

1 Like

Adhere - Definitely Writing

Feb 19, 2025 at 1:36pm
In response to "Fail to Succeed"

Having drunk soda on both sides of the Atlantic, I have to say that Mountain Dew with HFCS in America tastes a lot better than the 'same' drink made with sugar here in the UK. The experience is smoother and so is the taste.

2 Like

tj wanderlust-words-in-motion

Feb 18, 2025 at 6:10pm
In response to "Tater Tales"

Instant potatoes? Yes, I enjoy them, too. We also use them for thickening up soups and stews.

1 Like

Robert Waltz

Feb 17, 2025 at 11:23pm
In response to "Linguistic"

Annette

- I appreciate the recommendations, but I canceled Netflix when the choice was to put up with ads for a lower price or pay a shitload of money. If it were free with ads, I'd manage like I did in the days of broadcast TV, but I flat-out refuse to both pay money and watch commercials, which is why I never had cable TV.

The price for the ad-free experience also went up to the point where it wasn't worth it with the amount I watched.

Annette

Feb 17, 2025 at 3:40pm
In response to "Linguistic"

I refer to my three languages as three different brains. In France, I activate my French brain. Which made for some funny turns of phrase when I was speaking to my son in English with English words, but in French syntax.

Netflix has some really good multilingual TV series. I recommend

Monsieur Spade

Black Spot

Capitani

1 Like

February 23, 2025 at 11:18am

#1084267

Revisited: "Forgive Me, For I Have Zinned"

For my weekly trip to the past, this time, we're not going very deep at all. In November of 2023, I wrote this for a blogging activity which is no longer with us, hence the "invalid item" link therein: "Forgive Me, For I Have Zinned"

The entry revolves around National Zinfandel Day,

which in that year fell on November 15 (the earliest it can occur, as it falls on the third Wednesday in November.)

I did a whole blog entry on these calendar events, just a few days ago. In brief, yes, I know a lot of them are just product promotions. This one's no exception; the website lists it as being founded by "Zinfandel Advocates & Producers (ZAP)," which is totally the name I'd come up with if I were putting together an industry coalition for zinfandel.

But then they had to go and make White Zinfandel, which is emblematic of everything that's wrong in the world.

So many of those emblems these days.

Now, to be somewhat fair, I've heard it's improved since the last time I had the misfortune of sipping it.

Nor have I had any in the time since that entry.

The first offense of white zinfandel is that it's actually a blush, or rosé.

True enough, but I don't think I was clear that this is an offense because it breaks the rules of wine categorization. Some rule-breaking is fine and necessary for innovation. This sort of thing just confuses people.

The second offense is that it's inoffensive. It's the wine equivalent of white bread, American cheese, and light beer: something seemingly crafted to appeal to the lowest common denominator, and I'm not low nor common nor a denominator.

Bland, characterless, etc. Apparently, white zinfandel was invented on accident by Sutter Home (which I always called Stagger Home). Other wineries produce it now as well, but the point is, it's unsurprising that white zin is as much an American product as all those other mass-market foods and drinks. Plus, I forgot to add, fake milk "chocolate."

And finally, the wine I tried when it was all the rage in the States was cloyingly sweet. (As I noted above, that may no longer be the case.)

How can I call it characterless and cloyingly sweet at the same time? Because I can.

Finally, "white" zinfandel tastes completely unlike the red variety, such that when I finally got around to tasting actual zinfandel, it was a real epiphany. I might actually like it better than Shiraz.

Jury's still out on that. I can say for certain, though, that I prefer both of those over cabernet sauvignon.

There was a bumper sticker floating around some time ago: "Absolve yourself of white zin."

I haven't seen white zin in stores for a while. Maybe it's just because I haven't been looking, but hopefully, it's at least partly because tastes have improved.

Given the continued presence of those other offensively inoffensive products, though, somehow I doubt it.

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