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Sunday, Mar. 9, 2025

3:45pm 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:

Soldier_Mike

about 15 hours ago
In response to "Story Time"

Causation vs correlation. Reminds me of the phrases we've all seen here on site with respect to comma usage (e.g. Come down and eat, children! vs Come down and eat children!).

1 Like

tj wanderlust-words-in-motion

a day ago
In response to "Just Teaming"

What about "teamMe"!

When I hear "team player" I also hear the boss expecting everyone to give 110%, then going back to the office instead of pitching it.

2 Like

🌖 HuntersMoon

a day ago
In response to "Just Teaming"

3 Like

tj wanderlust-words-in-motion

a day ago
In response to "One Fine Thing"

Soldier_Mike

recently I asked on of my grandchildren if she new what an octothorpe was (she uses hashtag) and after a minute of deep thought replied, "A mythical creature."

1 Like

Soldier_Mike

a day ago
In response to "One Fine Thing"

Regarding your Exclaimer!, I never heard the term octothorpe before; it was, as you point out, either pound or number (sign) in my experience. As an aside, it's only visually similar to, not identical to and interchangeable with, the musical sharp sign. The octothorpe's left-to-right lines are horizontal, while the similar lines on the sharp sign are slightly angled from lower left to upper right (# vs ♯).

2 Like

tj wanderlust-words-in-motion

Mar 7, 2025 at 2:25pm
In response to "Story Time"

It is amazing how you can give some people solid facts and they will doubt them, but make up a story filled with fallacies and they will believe it.

1 Like

Elisa, Stik of Clubs

Mar 7, 2025 at 9:44am
In response to "Story Time"

I might do my own commentary on this article, but for now, I will tackle one part.

The science of vaccinations and immunization schedules also seemed impenetrable. “I was very conflicted, and felt like: ‘I don’t know any of this stuff, I didn’t go to school for this,’” she says.

I struggle with this a lot. I really do. Part of me struggles because while science wasn't my strongest subject in school, I still did reasonably well in the various fields I did study. Biology happened to be my strong suit there, although I strangely managed to hold my own when I took intro to physics. That said, in my science education we didn't go over specific vaccination schedules or anything like that. However, between learning how vaccines worked and getting a halfway decent statistics education (a college semester and several introductory lessons in high school) I could draw the connection of vaccination schedules. So while people may think they didn't go to school for things like this...they might have without knowing it!

The other part of me wonders about the effectiveness of science communicators. This field admittedly is still pretty new (only gaining steam in the last decade). On the other hand, how effective are they in getting laypeople to truly pay attention? I feel like some of their work tends to kind of preach to the choir. I wonder if many of these communicators lean more on the science part rather than the communicating, and that's where things go awry.

4 Like

tj wanderlust-words-in-motion

Mar 6, 2025 at 1:59pm
In response to "Shhhhhhh"

I may have a slight allergy to delusional people; they give me a headache.

1 Like

Wordsmitty ✍️

Mar 6, 2025 at 12:40pm
In response to "Shhhhhhh"

I drove by that several decades back either coming or going to a vacation somewhere beyond. It's so strict that even birds couldn't tweet there. (someone had to say it)

2 Like

BIG BAD WOLF is Merry

Mar 6, 2025 at 9:29am
In response to "Shhhhhhh"

Always someone complaining about something, annoyingly.

1 Like

February 4, 2024 at 9:04am

#1063436

Revisited: "Poker"

As has become my usual habit on a Sunday, I picked an old blog entry at random to see what's changed. And boy, did I hit an old one—only the fourth entry, in fact, from early January, 2007: "Poker"

This was back when I thought the blog would be about personal updates, as if my life were interesting enough to provide daily updates. Actually, it was "back when" a lot of things. Point by point:

Poker Night - dustbin of history

obligations in December - not any more

wife - no longer

my former groomsmen - see below

employee - I'm retired and he's long gone

wife's friend's husband - dumped his wife, ran off with a younger belly dancer

Quintessential gin - no longer available in Vir-gin-ia

Final verdict: 0/7

With qualifications.

The qualifications are thus:

I'm still in contact with one of the groomsmen, though not both. Actually talked to him last night as we were gaming.

While Quintessential is unavailable to me (it really is my favorite gin, though others come close), one thing that has not changed in 17 years is drinking itself. Well, maybe not quite as often. But it's nice to have some consistency in my life.

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