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

February 27, 2007 at 7:57pm

#491047

Disturbed

Nothing like a good old-fashioned pissedoffedness to break me out of my blue funk.

http://www.kait8.com/Global/story.asp?S=6135202

Simonton told police that she had been pistol wipped and raped with a screwdriver by a Hispanic man after she picked him up on the side of the road carrying a baby. She later confessed to authorities that her facial injuries were self-inflicted and that she had made the entire story up.

I'm reading this and I'm thinking, yeah, this kind of thing is fucked up, and unfortunately it happens from time to time, and yeah, I'd say she's mentally disturbed.

Then I got to the last paragraph.

One study from Purdue University found in over 40% of the rape cases they studied, the so-called 'victim' in those cases, like Simonton's, eventually admitted that no rape had occurred.

What?

"Over 40%?"

Leaving aside for the moment the questionable value of a single survey statistic stuck in as a throwaway at the end of a news story, I still have to consider this pretty damn disturbing.

Back in the Stone Age (my first marriage), I was sitting watching TV with my then-wife and this PSA came on. One of those that consists of a single, disturbed, worried and slightly haggard-looking woman, speaking as the camera zooms slowly in on her face. "Every fifteen seconds in this country," she said in all seriousness, "a woman is raped."

"Boy," I said, "she must be pretty sore."

I nearly became a statistic, myself. I'm pretty sure my ex-wife would have killed me if I hadn't outweighed her.

Point is, women don't find rape funny. I don't blame them. For some reason, though, both men and women find male-on-male rape pretty damn amusing. "Boy, you look just like a hog!"

As under-reported as rape is supposed to be, male-victim rape is probably even more underreported. "Uh. Yeah. I was walking down the street and this guy grabbed me and shoved his cock up my ass..."

"Sir, what were you wearing?"

Yeah, like I said: not funny.

I have to wonder about the fifteen second statistic, too. Math time. There are 24*60*60/15 = 5760 fifteen-second intervals in a day, which means according to the very serious woman on the PSA, about 5800 women get raped a day (assuming none of them are gang-bangs). That's 5760*365= about 2.1 MILLION women per year.

Okay, now I'll admit I'm in over my head. That's a lot of assaults, even if you can accept that over 40% of them are false reports. So let me get back to my original point.

Couple years back, a local man was charged with rape based on a woman's testimony. As I recall this case, there was no controversy over whether the woman was actually raped or not; her situation and story were consistent with violent sexual assault. In keeping with the privacy customs of our country, the woman's name was withheld from the press, while the man's name was widely reported.

Well, it turned out that she'd picked the wrong black male out of a lineup. I guess they all looked alike to her or something. In any event, this guy had to endure, at a minimum, massive legal expenses, and probably a whole load of underreported social expenses. Imagine how people would react to you after your name is plastered all over the papers in connection with a violent sexual assault - as the perpetrator. Especially in the southern U.S. if you're African-American.

Well, he was cleared, and he sued the chick, and the media had a freaking field day. "It should be illegal," was the consensus of certain groups, "to sue a person for damages after a false accusation of rape! Rape is underreported as it is, and it would have a chilling effect on women coming forward and reporting it!" No mention of the "rights" of the falsely accused to clear his name, or the chilling effect lawsuits would have on false accusations. After all, he's only a man, and if he didn't commit this rape, obviously he committed another one. How else do you explain 2 million rapes a year?

Do I have an easy answer? Of course not. I'm just ranting.

I'm going to stop now. I have a deadline and need to go back to work. But I'll leave you with this little gem:

http://news.yahoo.com/s/ap/20070225/ap_on_hi_te/smart_surveillance

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