Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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:

QPdoll

about 13 hours ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

about 16 hours 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

a day ago
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

a day ago
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

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

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

2 Like

Aiva Raine

a day ago
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.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

September 4, 2023 at 10:43am

#1055136

Astronomy

It's Labor Day here in the US, and I have an aversion to labor, so today's comments will be brief.

The 8 Best Astronomy Books For Beginners
From Mary Roach’s hilarious look at space travel to astronaut Scott Kelly’s photos documenting a year off planet.

Usually, Atlas Obscura highlights interesting locations here on Earth. This represents a bit of an expansion of their purview.

It’s easy to forget amid summer road trips and back-to-school to-do lists that our Earthly home is just a floating speck of blue in the vastness of the universe, that our human lives are just a blink in our galaxy’s long history.

It should be easy to forget. No matter how insignificant we may seem, we're the ones figuring this shit out, and that's pretty awesome.

Even if you’re completely new to the topic, these books are accessible, moving invitations into the furthest reaches of our cosmos.

I'm anything but new to the topic, but one cool thing about astronomy is that there's always more to learn.

I haven't read any of these books. They seem interesting enough, though they're not all technically about astronomy.

Since there's not a lot of point to copying the book titles and summaries—they're right there in the link, and the summaries are elevator-pitch length—this is as good a time as any to do one of my language investigations.

Before astronomy, there was astrology. Astrology is, rightly, considered pseudoscience at best, complete horseshit at worst. I fall somewhere in between; I look at it the same as I view folklore. It's an interesting window into psychology and human history.

Which leads me to the language bit. Other legitimate branches of science use the -ology suffix: psychology, biology, geology, zoology, etc. It can also be used to describe questionable fields of study, like theology, demonology, or UFOlogy, perhaps lending these subjects a false aura of science. The suffix itself, obviously, comes from the Greek "logos," which as I understand it just means "word" (which doesn't explain why a "logo" is often just a pictogram).

Astronomy is different, then, in the use of the "-nomy" suffix, which, according to the usual sources, means something like arranging or categorizing. But it's not alone. You also have taxonomy, which has nothing to do with paying the government money and everything to do with categorization; economy, which is notoriously slippery to define; gastronomy, which is kind of related to today's link because Atlas Obscura also hosts Gastro Obscura, a series of articles about the wonders of food (I've linked those a few times); and not many others. Anomy, however, refers to a lack of moral or ethical standards, which, what? It's also spelled anomie because English is had to pin down, sometimes.

Had the history been different, perhaps "astrology" would be the science while "astronomy" would be the folklore. We'll never know. But one reason I can't fully dismiss astrology as a subject is its place in history. Even Newton, known for his discoveries in science and mathematics, started from a foundation of astrology and alchemy. Just to be clear, though, I don't "believe in" it; I just find it interesting, same as with the folklore surrounding cryptids.

Astronomy can be defined as the study of celestial objects, and this is why it's kind of fuzzy to define in practice: Earth is, itself, a celestial object. One of my favorite websites, which I've visited nearly every day since it began in 1995 and which hasn't changed format much in those nearly three decades, is the Astronomy Picture of the Day

—and it often features images of Earth alongside investigation of faraway planets, stars, nebulae, and galaxies.

Which leads me back to the original link, because some of the books there are really about Earth. And that's okay; our -ologies and -onomies are all interconnected, anyway.

3 Like • Comment • View 1 comment

© 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.