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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🌝 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.

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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

June 1, 2008 at 8:26pm

#588465

Hopping MADD

Many juniors and seniors were driven to tears - a few to near hysterics - May 26 when a uniformed police officer arrived in several classrooms to notify them that a fellow student had been killed in a drunken-driving accident.

The officer read a brief eulogy, placed a rose on the deceased student's seat, then left the class members to process their thoughts and emotions for the next hour.

Pause a moment to think about this. You're a high school student, and someone comes in and tells you a classmate has died a horrible death. Then:

About 10 a.m., students were called to the athletic stadium, where they learned that their classmates had not died. There, a group of seniors, police officers and firefighters staged a startlingly realistic alcohol-induced fatal car crash. The students who had purportedly died portrayed ghostly apparitions encircling the scene.

http://www.theagitator.com/2008/05/31/absolute-maddness/

Now, I'll be the first to acknowledge that drunk driving is Bad. I certainly go out of my way to get quietly drunk at home, or someplace where I know I have a ride, rather than getting in a position where I might even consider it.

But MADD can kiss my gin-soaked ASS. I know the idea is to mess with kids' heads - and I heartily approve of messing with kids' heads, but not like this. We're talking years and YEARS of therapy, here.

And what about the bastard kids who actually went along with this charade and let their classmates think that they're dead? I mean, I vaguely remember when I was in high school, I was like, "I wonder if they'll care if I'm dead. Maybe I'll stage my own death and make them think I'm gone, and see who actually cries. Yeah. Then I'll find out who really cares about me." Teenage angst crap. Well, here's a bunch of teens who actually got to live that fantasy - with help from the teachers and the fucking cops!

And then - what happens when someone actually dies in a car wreck, alcohol-induced or not? It happened to at least one kid every year when I was in high school, and the other kids were all shocked and saddened, even the ones who didn't particularly like the deceased. But now, these kids are going to be like, "Yeah, whatever, another stupid MADD stunt."

As the blogger in the above link said, "What the hell is wrong with these people?"

I'm telling you what, I don't drink enough to put up with this shit.

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