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:

🌖 HuntersMoon

about 23 hours ago
In response to "Paint in the Neck"

Given the current situation, maybe they'll update their logo... by changing the paint color to orange.

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Revisited: "Bloomington""

I have been to Bloomington a few times myself, the one in Minnesota, not Illinois or Indiana.

2 Like

🌖 HuntersMoon

a day ago
In response to "Revisited: "Bloomington""

You and Jim look just the same as I remember. Hmmmmmm. I was hoping my memory was fading but no.

1 Like

tj wanderlust-words-in-motion

Feb 8, 2025 at 4:58pm
In response to "What's In a Name?"

It seems no matter what, someone will be offended by it. Even if no one is offended, someone will become offended that no one's offended. Maybe we should bring back All In The Family.

2 Like

🌖 HuntersMoon

Feb 8, 2025 at 9:30am
In response to "What's In a Name?"

Shhhh! Let's hope one of the Great Pumpkin's minions doesn't see this. You may get banned on the basis of... promoting transgenderism, exploiting children, or whatever the hell they come up with.

2 Like

tj wanderlust-words-in-motion

Feb 7, 2025 at 4:26pm
In response to "Roll Model"

Most commercial-grade wipe is like trying to clean one's bum with super-thin wax paper! When I see "Mega-Roll" I instantly realize it will not fit into the holder. I don't put a lot into buying butt-wipe, I stick to one product I know will fit the holder, clean the crap, and my fingers won't bust through.

1 Like

tj wanderlust-words-in-motion

Feb 6, 2025 at 3:24pm
In response to "So Much Energy"

I always thought electroweak{i/} was a bad choice of terminology. It sounds like the batteries in you flashlight are almost dead! They should have used a term like "electronuke" which sounds like some super-hero stuff. There's no need to fear, Electronuke is here!"

Also, when crossing Higg's field, beware of Higg's boson (cross between a boar and a bison) or you may get killed; unless of course, Electonuke shows up and saves your ass.

Alright, maybe I should be writing a story instead of leaving a comment...

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Graham B.

Feb 6, 2025 at 12:04pm
In response to "So Much Energy"

The only energy-carrying particle that concerns me is the Joeson, as in "I need my morning cup of Joeson to get me up." It's responsible for the strong nootropic force (for me, anyway).

3 Like

Lazy Writer est 4/24/2008

Feb 6, 2025 at 11:36am
In response to "So Much Energy"

I need to find some of that energy..because mine is worn out!

2 Like

tj wanderlust-words-in-motion

Feb 5, 2025 at 4:33pm
In response to "That Healthy Glow"

Yes, they do still make black lights, most are LED. We have one above my wife's plants, it helps them survive through the winter with our lack of sunlight. They seem to be more purple than the black lights from days gone by. Interestingly, they make our Australian Shepard glow purple (her black areas) and they make our Husky's blue eyes glow, but not the black on his fur.

1 Like

February 10, 2025 at 7:55am

#1083630

Paint in the Neck

Logos are kind of the corporate equivalent of a book's cover art, so writers might be interested in this sort of thing from Fast Company:

The world’s worst logo also happens to be its best
Even after 120 years, the Sherwin-Williams ‘Cover the Earth’ logo is so bad it’s good.

Calling something "worst" or "best" is, at best, hyperbole. But we shouldn't just brush off the ideas here.

Every time I see the Sherwin-Williams logo, my brain briefly and hopelessly breaks.

I have a very clear memory of myself as a very young kid, seeing that logo for possibly the first time, and thinking, "What? That's not how gravity works!" So my mental break was based on the clear violation of the immutable laws of physics, not the questionable violation of the ever-shifting laws of graphic design.

And like any good intoxicant, I enjoy it. Because it is, hands-down, one of the worst logos in all of existence—but also one of the all-time greats.

Speaking of marketing, please take note: that quote hedges with "one of the..." before the superlatives. It does not claim that it is somehow objectively the worst or the best. The sentence is clearly both opinion (that of the author) and allowing for reasonable people to argue that, no, there might be a worse logo or a better logo. This is in stark contrast with the headline—you know, the marketing part of the article—which declares with no uncertainty that it's both "worst" and "best," absolute, no nuance, no argument possible.

For the uninitiated—and there’s no delicate way to put this—the Sherwin-Williams logo features a moon-size bucket seemingly drowning the Earth with a quadrillion gallons of *blood-red* paint, wholly saturating it to the point where its runoff is in nation-size droplets.

1) the paint can looks to me to be bigger than the Moon at that scale, but okay, maybe they meant "moon" in generic terms.
2) I'd like to do the calculations to see if you'd really need a quadrillion gallons to literally cover the Earth, but I can't be arsed.
3) Nations vary wildly in size, so calling something "nation-size" doesn't mean much.

These things matter more to me than marketing fouls.

And yet, you may be wondering, as I do every time I peruse a hardware store: How in the name of God is that still the company’s logo?!

Well, no, I find it comforting that some things don't change.

And maybe we should celebrate that an anachronism as bold and bizarre still exists (not unlike my other favorite dinosaur-of-a-logo, the, um, Sinclair dinosaur).

The problem with the Sinclair dinosaur is that it reinforced the false idea that crude oil came from dinosaurs. I suppose it's possible that the SWP logo warped some peoples' understanding of gravity, but I don't think that falsehood is nearly as widespread as "oil is dead dinosaurs" myth.

There's a bit more at the link, including a brief history of SWP and its logo, and even more pics of the logo in question (the one I linked earlier is from a different site). I think it paints an interesting picture.

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