Complex Numbers (Book)

Blog Calendar

◄ January ► 2023
S	M	T	W	T	F	S
1	2	3	4	5	6	7
8	9	10	11	12	13	14
15	16	17	18	19	20	21
22	23	24	25	26	27	28
29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

Complex Numbers

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:

Writer_Mike

about 13 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

Sep 21, 2024 at 7:34am
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:46am
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

January 17, 2023 at 12:01am

#1043234

Ice Empress

At some point, I think it was last year, I finally got around to watching Frozen. What can I say? Without kids, I was never forced to, but it's part of my Disney+ subscription, so at least I didn't have to pay more for it. (Still haven't seen the sequel.)

As usual, though, truth is stranger than fiction.

The Time a Russian Empress Built an Ice Palace and Forced Her Jester To Get Married In It
Cruel joke, power move, or both?

Now, the truth is, I don't have much to say about this beyond the Frozen reference above. I just thought it was—to understate things a bit—cool, so here it is, shared.

It was 1740 and one of the coldest winters St. Petersburg, Russia, had ever seen. But few residents mentioned the bitter winter in letters or accounts. They were, understandably, distracted. While the rest of Europe shivered through the deep freeze, Russians were busy—building a palace. On the orders of Empress Anna Ioannovna, numerous craftsmen were charged with constructing an elaborate, fairy tale–esque castle, one made entirely of ice.

On the plus side, I suppose the exertion kept them warm. And the fear of being executed for underperformance, but mostly, the exertion.

Rising 66 feet from the surface of the frozen Neva River and nearly 165 feet long, the Ice Palace was built “according to all the rules of the most current architecture,” noted Russian mathematician Georg Wolfgang Krafft.

I guess one of the rules wasn't "don't build your palace out of ice."

A steam bath, or bania, built from ice sat beside the palace. Decorative ice dolphins blew fire. A life-sized ice elephant’s raised trunk served as a fountain by day and as a stunning torch by night.

Gotta say I'm impressed by the violation of the laws of thermodynamics, which, to be fair, hadn't been formulated yet.

The palace was, by all accounts, a marvel. But the elaborate, temporary palace isn’t the strangest part of the story. That winter, Anna ordered a bizarre wedding to take place at the Ice Palace between the disgraced noble-turned-jester, Prince Mikhail Golitsyn, and a Kalmyk woman, Avdotia Buzheninova.

Okay, I had to look up "Kalmyk." Apparently a Mongol ethnic group in Russia. The article does explain this later, but I hadn't gotten to that part yet. I'm sure their story is fascinating, too, but I'm short on time tonight.

“The nobles choose Anna because, as a woman, they think she’ll be very easily manipulated,” says Russian historian Jacob Bell of the University of Illinois. The nobles imposed a list of conditions (creatively dubbed the “Conditions”) on Anna’s power and made her sign on the dotted line. She signed, but Anna was far smarter than they gave her credit for.

Within a couple of months, Anna solidified support from a group of nobles and the local guards’ regiments. “[She] then, very dramatically tears the conditions in half and declares she will rule in the way she wants to rule,” says Bell.

This is one of the most Russian things outside of depression and vodka.

Continuing many of the efforts begun by Peter the Great, she funded the Russian Academy of Science and encouraged Westernization. She founded the Cadet Corps, a premiere military training school, and maintained a brutal secret police known as the Secret Office of Investigation.

The Russianness intensifies.

Ahead of the nuptials, Anna decreed every Russian province to send a man and woman wearing traditional dress to attend the spectacle.

I suppose at least she didn't make them all wear ice?

With all of this sort of thing going on, it's surprising that it took over 150 years after the Ice Palace incident for Russians to rise up in revolt. I guess they might have started to, but got cold feet.

3 Like • Comment • View 3 comments

© Copyright 2024 Waltz en France (UN: cathartes02 at Writing.Com). All rights reserved.
Waltz en France has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.