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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:

Write_Mikey_Write!

a day ago
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

a day ago
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

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

October 19, 2021 at 12:03am

#1019641

Man

I can admit when I just don't understand something. This is one of those times.

How to be a man
Old ideas of manliness make us miserable. Being labelled ‘toxic’ doesn’t help. A reimagined masculinity is the way forward

As is often the case for these things, the author is basically trying to sell his books. I've noted before that this is not necessarily a bad thing, especially since a lot of us are writers. The techniques used for selling books are writing exercises in themselves.

That said, I still don't fully understand this. I don't know whether it's because I'm completely stupid when it comes to such topics as emotions, gender identity, and how to relate to other people, or if it's a really clever marketing thing: "If you want to know more, buy my book!"

And that’s what is needed to be a man today: the freedom to customise one’s gender identity and not be forced into what’s on the rack.

I think that's how I live my life? Mostly? I don't know.

One essential article we all need in our wardrobe is emotional resiliency.

And I probably should have stopped reading there, because I don't have a good idea about what that actually is.

We might still buy into the beliefs that we’re supposed to avoid asking for help and that we should not talk about our fears, sadness or emotional isolation.

Maybe because talking about such things is a great way to become even more isolated? There is very little more unattractive than depression and loneliness, so admitting to those things is a surefire route to becoming more depressed and lonely because people scatter like roaches in the light.

So I'm not going to say much more about the article. It's fairly long and I'd understand if you didn't want to read it. I did, and then I had to go watch videos on quantum physics and mathematics because I understand them better.

But I'm putting it here in case a) someone has some insight and b) something sinks in with me and I can go back and revisit it at some later date.

Mini-Contest Results!

I enjoyed all the comments yesterday. Hard to pick just one word, right? Considering the different pronunciations of, for example, through, tough, trough, and thorough, it's a wonder anyone can learn English at all. Some of you mentioned "knight;" I've heard that the word used to be pronounced more like how the French Persons in Holy Grail said it: k'nigk't, or something similar to that. The K and the GH ended up becoming silent and the vowel lengthened. Don't ask me how or why. People are weird.

But yeah, place names are probably the worst. I'm reminded of the town in Indiana called Versailles. Anyone with even a passing familiarity with even the slightest bit of French (or some knowledge of WW1) knows to pronounce it like "ver-sigh." But no, not in Indiana, where you have to call it "ver-sails" or they run you out of town on a ryel.

So today's MB goes to Pumpkin Spice Sox

for the place name nonsense.

We'll do this again soon.

5 Like • Comment • View 5 comments

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