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, Snowman Stik

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, "keep on keeping on!"

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, "keep on keeping on!"

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 Robert Waltz?

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 Pon

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 Merry

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

July 1, 2008 at 7:06pm

#594102

Ah... Schadenfreude.

For those who've been living under a rock (or victims of the US public school system), schadenfreude means roughly "delight in another's suffering" and is a loan word from German, which is the only language in the world that could possibly have a special word for that. Except maybe Russian, which as far as I know, doesn't.

Today's schadenfreude is brought to you by Starbucks. You remember Starbucks, the folks who somehow built a business model out of selling $8.00 cups of coffee, thus invoking another loan word, this one from Yiddish.

Well, this amused me:

http://seattlepi.nwsource.com/local/6420ap_wa_starbucks_closings.html

SEATTLE -- Starbucks has announced it's closing 600 underperforming stores in the United States.

The Seattle premium coffee company also announced Tuesday it expects to open fewer than 200 new company operated stores in the United States in fiscal 2009.

You may recall my Starbucks rant from a few days ago: "Starbuck's"

, with links to the eight (8) types of annoying people you'll find in Starbucks.

So, all I can say is: HAHA!

I mean, come on... The Onion wasn't far off a few years back when it ran an article about how Starbucks opened a new store on the way to the restroom at a Starbucks. You can't spit in NYC without hitting one of the pretentious coffeehouses. Sometimes they're on opposite corners of the same bloody intersection.

Okay, I hope the people working there can find work elsewhere, but I feel no sympathy for the management. Maybe instead of closing unprofitable stores, they could help profits by reducing prices to something you don't have to feel pretentious to pay, thus gathering potentially more customers, but apparently not...

Speaking of schadenfreude, I just had to post this pic of the train wreck that used to be a singer with a formidable voice:

http://wwtdd.com/post.phtml?pk=8621

Three days ago, Amy Winehouse left the hospital after being told that if she continued to do drugs and smoke and drink, she would die. Amy didn’t do any sort of rehab, then walked out of the hospital and onto the path to salvation. With a cigarette in her mouth.

You go, Amy. Don't let the bastards get you down.

Did I say trainwreck? Maybe "horsewreck" would be more appropriate.

Those tattoos on the Wino's arms reminded me of the Cracked contest involving what tattoos would be like if they actually told the truth.

http://www.cracked.com/article_16446_if-tattoos-actually-told-truth.html

When you look at someone's tattoo, all you really know about that person is that they have low self esteem and at least enough money to purchase a tattoo. That's pretty much it.

Well, we told you to show us what tattoos would look like if they were honest, and you did. If more people got tattoos like these, it'd be quite a time saver.

While we're looking at my favorite snark site, where the writers are even funnier than I am (try to imagine it), I found this synopsis of 6 Famous Songs That Don't Mean What You Think to be endlessly hilarious:

http://www.cracked.com/article_16442_6-famous-songs-that-dont-mean-what-you-thin...

Sometimes, the more you know about a song the less you enjoy it. You start out thinking the singer of some ballad totally identifies with your situation, then later find out most musicians are creepy sex maniacs, and boring at the same time.

...

It's a well known story that in 1984, Ronald Reagan's campaign for reelection tried to use Bruce Springsteen's blue collar protest anthem "Born in the USA" as a rallying cry. By now, most people understand that a song about a Vietnam Vet who ends up unemployed and in jail isn't exactly an endorsement of trickle-down economics. What you might not know is that you probably made the exact same mistake as Reagan about the admittedly less awesome John Mellencamp song "Our Country."

Okay, so I used an excuse to quote a part that, while not exactly endorsing Springsteen, at least doesn't mention him in a negative way.

So that's about it. Sometimes I just have to look elsewhere for material and, fortunately, the internet never fails to provide a plethora. It was either that or get drunk and listen to Brandi Carlile.

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