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

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Stik-or-Treat

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

tj says Boris sent me

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

tj says Boris sent me

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Waltz in the Lonesome October?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pumpkin

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Howling

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

August 5, 2022 at 12:03am

#1036122

Logos

I have only a passing interest in marketing, and suck at graphic design, but I find logos interesting. So, apparently, does Cracked.

The Bizarre Origins of 15 Famous Logos

"Bizarre" is too strong a word here, but such are clickbait headlines. You won't believe what happens next!!!

In the quest for that perfect logo that will stand out but not in a bad way, companies have reached back into the scary, briny depths of human creativity, taking inspiration from everything from strip clubs to Greek gods.

So there you have it: the answer to the question (which nobody ever asked), "What do strip clubs and Greek gods have in common?" (Other than "Both will smite you if you put your hands somewhere you shouldn't.")

I'm not quoting all fifteen here. Just the ones I have something to say about.

14. Chupa Chups

You’d never know it from the lack of ants or anything decaying, but the Chupa Chups lollipop logo was designed by Salvador Dali during his “anything for money” phase in 1969.

This one, I knew. (Actually, I think I knew most of them, but there's always something else to learn.)

12. Starbucks

Hopefully everyone knows by now that the original "mermaid" was bowdlerized to appeal to prudes. What might be news is where the big-titted mermaid originally came from.

It probably actually came from the artwork in a 15th-century German book.

"Probably?" Okay.

Speaking of titties...

11. McDonald’s

The golden arches were adopted as an ode to the ones that framed the original restaurant, but they were kept because they were Freudian. During a branding overhaul in the ‘60s, one psychologist advised them to keep the logo because it “symbolized a mother’s nourishing breasts.”

We're talking about two of the biggest franchise chains in the US, and thus the world. The moral of this story is: boobies work.

9. Michelin

This mind-blowing about the Michelin Man comes in four parts: 1) He has a name. 2) That name is “Bibendum.” 3) He’s made of tires. 4) He partied like a rock star. Early advertisements featuring the Michelin Man from the late 19th century often depicted him smoking a cigar and drinking champagne...

I think they accidentally a word there. Also, the Michelin Man is apparently a badass. Or was, until they turned him into a marshmallow.

8. MGM

The first MGM lion was apparently such a beast that he was buried under a marble slab to “hold down the lion’s spirit,” as if it might leap out and turn someone awesome via possession, but that’s nothing compared to the next one, who was the first to actually roar.

As far as corporate logos go, it's hard to beat an actual lion. (Food Lion, aka Shitty Kitty, doesn't count.)

Why hasn’t Marvel given this guy a movie?

For the same reason Cracked doesn't do an exposé on Alfred E. Neuman: competition. Marvel is owned by Disney, and the Mouse has more lawyers than a lion can eat.

3. Facebook

“Blue is the richest color for me -- I can see all of blue,” he later explained, because that’s Mark Zuckerberg’s top business concern: Mark Zuckerberg.

Colors aside, I always hated the facebook logo's font.

1. Gucci

Those two interlocking G’s don’t just stand for the brand name -- they’re actually the initials of the founder. Yes. The poor man’s name was Guccio Gucci.

And based on the movie House of Gucci (an MGM film, incidentally), you could probably power all of Florence if you attached a dynamo to his spinning corpse. To be fair, insiders have said the movie's not accurate, but at least you got to see Lady Gaga's boobies.

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