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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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

a day ago
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.

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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

Robert Waltz

Feb 17, 2025 at 12:00pm
In response to "Linguistic"

Kåre เลียม Enga

- yeah, I edited out the duplication, because it could be seen as a refutation of itself.

1 Like

Kåre เลียม Enga

Feb 17, 2025 at 11:32am
In response to "Linguistic"

I use translation tools all the time... and subtitles on youtube.

My French pronunciation is okay because I learned it as a child; my Spanish is okay because I practiced it. I slip into both with one key exception. French is easier when I'm depressed and Spanish can draw me out of depression.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms.

Yes, I saw that you repeated that. It bears repeating.

Speaking multiple languages has also been linked to delayed onset of dementia symptoms. Or so I hope.

1 Like

February 22, 2025 at 10:02am

#1084231

Apparatus

First, an Exclaimer! ▼

#roosterapparatus

There are things I've wondered about since I first encountered them, and that curiosity was so powerful that I researched it. This was harder in the old days, before the internet made such research simultaneously easier and less reliable. One of the things I wondered about pre-internet was why it is that a rooster crows, but a crow never roosters. But I didn't care enough to look it up.

What I did try to find out, at some point, was why one could use either 'cock' or 'rooster' for the male poultry specimen. As it turned out, the latter word was apparently a US invention, attempting to avoid one of the more salacious meaning of 'cock.' Typical US. If the euphemism origin is true, it would be one of those relatively rare occasions when a euphemism doesn't eventually take on the same connotations as the word it replaced. That is truly weird, as that particular body part is of such paramount importance to the world that almost any word, and several gestures, can, depending on context, refer to it.

One thing I have never attempted to find out, despite having lived on a farm, is how chickens reproduce. At least, apart from the obvious and clichéd chicken / egg cycle. I just didn't care, partly because we didn't have chickens and partly because I just didn't care. But you pick up things here and there, so I know more about the process than I really wanted to.

All of which is to say that roosters don't really have an apparatus as we would identify it.

As per the Exclaimer! up there, the tag in the title, apparently a smushing of rooster and apparatus, is banned on a certain social media platform, but it doesn't seem to be because of its reference to the nonexistent cock cock. No, a brief search revealed that the words refer to a business that sells artisanal glass products which may or may not be pressed into service for smoking the devil's cabbage.

Whether the association with the natural substance which is still illegal in most places is the reason for the ban, or maybe they're just a shady company using legitimacy as a kind of smoke screen, or perhaps something else entirely, the name really is a good one. Not because of chickens or cocks, but because, as my Google search revealed, there aren't many other uses for the particular combination of "rooster" and "apparatus." Memorable and unique; good company name, though I'd have never guessed the product from the tag name. I guess maybe I was expecting it to refer to weather vanes, the clichéd depiction of which almost always involves a rooster.

But no. Not dongs or schlongs, but bongs.

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