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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 in a winter wonderland

about 17 hours ago
In response to "Neutral Zone"

I don't tend to think of myself as optimistic or pessimistic, although I do share some of both qualities; I'm realistic.

1 Like

tj in a winter wonderland

about 18 hours ago
In response to "Allo, Ow Arya?"

heightened and delighted attention—Hedention

1 Like

tj in a winter wonderland

a day ago
In response to "Retraction"

Another interesting entry, thank you. As for the Committee for Bug-Free Food, I have also read some of the information on insects in canned foods. I always wonder how that compares to insects in frozen food, vacuum sealed foods, and irradiated foods. I grew up eating fruits and berries right off the tree/shrub/vine and likely consumed a fair number of insects without even knowing it.

2 Like

Jayne

a day ago
In response to "Retraction"

Wow, 8 retractions in a month + 60 concerns this year. They should get a new journal tagline:

Chemosphere, the vanity publisher for "science".

"Awesome science journal" - Reddit User RandomDude02342

3 Like

tj in a winter wonderland

Dec 31, 2024 at 4:48pm
In response to "The End of December"

I'll drink to that.

2 Like

Elisa: Snowman Stik

Dec 31, 2024 at 11:07am
In response to "The End of December"

The story behind Dry January (which actually started in the UK) is part typical insufferable but also part fascinating, as it serves as a bit of reckoning with the drinking culture over there. It may be a bandwagon thing, but given how alcohol has legitimately killed people I can see how it's caught on.

3 Like

🌖 HuntersMoon

Dec 31, 2024 at 10:02am
In response to "The End of December"

At last! A resolution I, too, can achieve!

2 Like

tj in a winter wonderland

Dec 29, 2024 at 4:16pm
In response to "Revisited: "None More Black""

Favorite color? Growing up it was deep red, but having a little brother, his favorite color also had to be red, so I decided to pick blue. His also turned blue, so I decided not to have a favorite, but to like all colors. But, what do you get if you mix together all the colors? Black.

Robert Waltz

Dec 29, 2024 at 10:34am
In response to "Revisited: "None More Black""

🌖 HuntersMoon

: See also my many polemics on the fruit status of tomatoes.

1 Like

🌖 HuntersMoon

Dec 29, 2024 at 10:21am
In response to "Revisited: "None More Black""

Knowing your penchant for "scientific" foundations for answers, black is not a color.

Black's status as a color varies depending on the perspective:

Scientific perspective: Black is not a color; it is the absence or complete absorption of visible light, making it an achromatic shade.
Artistic perspective: In art and design, black is treated as a color because it can be created by combining pigments and provides contrast.
Human perception: Black evokes feelings similar to other colors and is often associated with darkness, power, and elegance.

2 Like

December 31, 2024 at 9:32am

#1081753

The End of December

Well, here we are at the end of another trip around the sun (or close enough), at a purely arbitrary date on a purely arbitrary calendar.

I had what I consider to be the beginning of the new cycle ten days ago, on the solstice. If anything should mark a transition on what's really a continuum, let it be something real and measurable. But, most of the world uses the Gregorian calendar for recordkeeping and consistency (it is, I'll grant, remarkably good at calculating solar returns), and it's one of the few things most of us share. So we want to impose meaning on December 31 / January 1, fine. Impose it. At least it's usually celebrated with two of my favorite activities: Drinking, and staying up late.

Now, I don't usually make resolutions. I think they're artificial, and set the resolutor (or whatever) up for failure. Besides, it's a bandwagon thing, and I hate bandwagon things.

Another bandwagon thing is the concept of Dry January: the idea of abstaining from ethanol during that calendar month, perhaps in penance for December's overindulgence. This concept legitimately offends me, and I don't get offended easily. In past years, I've simply ignored it and gone on doing what I usually do.

Thing is, contrary to popular belief (that I promote), I don't actually drink every day. Usually once or twice a week. More, perhaps, when I'm on a trip, but only if I'm not subsequently driving. But this New Year's, I've decided to throw personal tradition into the trash and actually make a (gasp) resolution:

Be it hereby resolved that, in protest of the abominable concept of Dry January, Waltz is determined to drink an alcoholic beverage every day during the calendar month of January. This could be a cocktail, a shot of tequila, a dram of scotch, a tot of rum, a bottle of beer, a glass of wine, or the equivalent. More than that is acceptable. Less is not. I do reserve the right to deliberately fail at the resolution in the case of illness or severe injury that requires painkillers, but apart from that, no excuses.

Don't get me wrong: anyone who genuinely wants to stop drinking, temporarily or permanently, as a resolution or otherwise, I wish them well. This is for me. I just have major issues with following a crowd or participating in what's probably little more than abolitionist propaganda.

We'll see how it goes. Knowing me, I'll fail at it like most of us fail at resolutions.

6 Like • Comment • View 3 comments

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