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Tuesday, Apr. 8, 2025

6:40pm EDT

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

tj wanderlust-words-in-motion

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 wanderlust-words-in-motion

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

Soldier_Mike

Mar 10, 2025 at 11:46pm
In response to "Revisited: "In Spite Of""

Tangentially related to 6. Adidas and Puma: During my first tour in Germany, I was assigned to the Army agency that formerly occupied Herzo Base, an airfield probably located within medium mortar range from the sport shoe factories.

As far as German revenge is concerned, I would venture a guess that it's planned down to the smallest detail and executed with appropriate gusto.

tj wanderlust-words-in-motion

Mar 10, 2025 at 6:31pm
In response to "Automatic for the People"

Earlier today I did a bit of shopping. I found a couple of items I had not planned on purchasing on sale so I grabbed them. As the cashier rang them up, I noticed they did not register the sale price, the regular price, but an even higher price. I questioned it and was told this, "The sale ended yesterday, but we didn't get the sign changed. Today the price increased because our cost has now increased." Yes, how did you guess, one of the items was eggs, now over a dollar each!

1 Like

May 16, 2021 at 12:04am

#1010240

For Better or Worse

PROMPT May 16th

What do you do to make the world a better place?

What, my mere existence isn't enough?

Seriously, though, I'm no judge of that. "Better" is a subjective quality. Sometimes what's good for one person or group is worse for another. We can't always know the full ramifications of our words or actions. As with the classic butterfly effect

in chaos theory, sometimes something small and insignificant can have huge consequences down the line.

Most times, though, the effects tend to dampen out and the end result is indistinguishable from random noise.

So, I don't know. I mean, I don't actively try to make the world a worse place. But when I think of anything I do to proactively improve things, I find my brain skittering away from the mere possibility of mentioning them. I would prefer not to shout virtue to the world. In fact, I take great pains to project an image of a selfish drunk who's only in it for himself.

Not that I haven't touted my own good deeds in the past, sometimes even in here. But I just never feel right about it afterward.

I guess I just feel like I'm often annoyed by the people who are like "Look at me! I give money to poor people! I help old ladies across the street! I only eat hyperlocal, organic, cruelty-free food! I'm so virtuous I make demons gnash their teeth in frustration and angels weep in jealousy!" And I don't ever want to be one of those people. Everyone has vices and virtues, and to proclaim one's virtues can make other people think you're hiding something horrid.

There are none so evil as those who claim to be virtuous.

There's another thing, too. Like, a lot of people, when they need to reference someone who is a Good Person™, they invoke the name of Mother Teresa. Mother Teresa was objectively a horrible person

who promoted the idea that Suffering Is A Good Thing, and the more you suffer, the closer you are to God. I have a word for people who promote suffering, and that word is: evil. No, she was a villain with a vast, powerful PR team. And yet a lot of people still think she made the world a better place.

So I prefer to keep such things to myself. People will spin anything I say or do the way they want to, anyway, and I'm not going to sit here and justify myself to others.

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