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.

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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!

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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

February 7, 2009 at 10:44pm

#634637

Subtletting

6. Subtlety is always lost on me, except when it's not.

I don't know. I think I'm a pretty straightforward kind of person. What I say is generally what I mean - humorous comments excepted.

I can also be passive-aggressive, but that doesn't translate too well to the internet, and I'm working on that little problem.

So to me, when someone says something, I'll generally take it at face value.

I know this woman who's single, never been married, rarely dates. When she does date, she debriefs to her friends - me included, if I can't plead a sudden need to wash my hair. No, she's no one on Writing.com, so quit wondering if it's you. Anyway, during these sessions, she replays every gesture, every nuance of speech, every word spoken, and analyzes it for hidden meanings. I don't know if this is a chick thing in general, or if it's mostly her, but the third time I heard her do this, I said, "You know, not every conversation is fraught with hidden meaning."

She squinted at me. "Yes, it is."

From that point on, I was very, very careful about what I said around her, how I said it, and what position my hands were in when I said it. And I'm glad I'm not dating anymore.

I have to wonder what it's like to live in a world where saying something like, "I'm hungry," for instance, means something other than "I'm hungry." I suppose it could mean, "Offer to cook me something," or "I want to go out to eat," or "I want to have mad, passionate sex with you." Or something else entirely. When I say it, I mean, "I'm hungry." When I hear my wife, or one of my friends say it, I think they mean, "I'm hungry." Sometimes they mean something else, and they look at me funny.

Maybe that's why I'm so lousy at poetry, and interpreting poetry. You can't take poetry at face value, not good poetry. Even with prose, the few classes I've taken on the subject overwhelm me with the analysis of All The Details and What They Really Mean.

I'm getting better at interpretation, but don't expect me to grasp the finer nuances.

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