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Sunday, Nov. 17, 2024

5:21pm EST

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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-turkey-jobble-jobble-hard-J

about an hour ago
In response to "Revisited: "A Frank Discussion""

I became disgruntled with meat sold in local grocery stores; half the weight is water, the taste is bland, and it's "use by" date is usually one day away. I found a small town butcher/locker plant that sells locally raised meats and buy in bulk so it's actually fresher, cheaper, and better tasting. Recently, I decided to try my hand at making our own sausage as well. It's a bit of work, but I think it's worth the trouble.

1 Like

Turkey DrumStik

a day ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

Nov 14, 2024 at 12:10pm
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

January 9, 2024 at 8:36am

#1062104

Journey to the New Word

From that ivory tower of knowledge known as Cracked, an article about words:

5 Words That Never Existed Till Oddly Recently

As December draws to a close, it’s time for the world’s dictionaries to name their Words of the Year.

Yes, this article was from last month.

Most words feel like they must have been around forever. But all words are made-up, and some of them were made-up pretty recently.

My goal in life is to make up a word and have it be widely used. I mean, sure, that's already happened: I came up with "rad" (the slang word, not the radiation level, which admittedly inspired me) back in the 70s. But no one knows it was me, and so no one believes me.

In fairness, someone else might have invented it independently. But I'm going with "they stole it from me."

Anyway. The article:

5. Boy

And yet, the word we have now for a male child, “boy,” isn’t that old. It only came about in the 16th century.

I've looked into this before. Maybe even here; I don't remember. Seems to me there's some debate about the actual origin. In this case, though, I didn't make it up.

Before that, for a few centuries, you know what we called male children? We called them girls. We also called female children girls. “Girl” was a unisex word.

I'm also unclear on the meaning of "we" here. 16th century would have been just after the end of Middle English.

Not to mention there were hundreds or thousands of words added to English since "boy."

4. Guy

For starters, the word was a name for around a thousand years longer than it was a common noun. Then came the big guy, Guy Fawkes.

Ah, yes, one of the prototypical religious terrorists.

To complicate things, I've heard this word pronounced both like it rhymes with "die" or rhymes with "key."

It now refers to people of all genders, though that final shift wasn’t so much a gradual expansion of its meaning as an assumption that any word for men can also represent all humankind.

No, that's not the assumption at all. We're moving away from that as a culture. The problem is that English now lacks a second person plural, and y'all won't adopt y'all, instead opting for "you guys."

3. Smoking

We say a fire is smoking up the place when it creates smoke, so it’s pretty weird that we say the same thing when we (or ham) take in smoke.

Not that weird at all. The smoke is happening whether you're inhaling or not, so sure, smoking is still being used in its older meaning, and this section is interesting but nonsensical.

2. Genocide

Gotta admit, the origin of this word surprised me. Specifically, that it's less than a hundred years old.

The word “genocide” was invented by one man: Polish lawyer Raphael Lemkin... The book was published in 1944. By 1948, the U.N. wrote up a treaty criminalizing genocide by name.

1. Forecast

Well, it's not like we needed a word like "aftcast." That would, however, be a fun synonym for "recent history."

By coining the term “forecast,” FitzRoy made the idea sound magical, which wasn’t particularly conducive to convincing skeptical scientists.

Sure, but I bet it got eaten up by the superstitious public.

So, yeah, just some fun with words. Nothing too rad, but I didn't want to just yeet the article into the dustbin.

4 Like • Comment • View 4 comments

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