Complex Numbers (Book)

Blog Calendar

◄ February ► 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
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 11 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.

February 2, 2023 at 12:01am

#1044036

A Star is Born

Not a lot I can say about this one; I just thought it was too cool not to share.

Before I get into it, though, a quick note: I'll be participating in "Journalistic Intentions"

[18+] this month (though not today). Check it out and join in—you have nothing to lose and everything to gain. Well, a couple of awards to gain, potentially, but that's not nothing.

And now, let there be light.

Astronomers Say They Have Spotted the Universe’s First Stars
Theory has it that “Population III” stars brought light to the cosmos. The James Webb Space Telescope may have just glimpsed them.

A group of astronomers poring over data from the James Webb Space Telescope (JWST) has glimpsed light from ionized helium in a distant galaxy, which could indicate the presence of the universe’s very first generation of stars.

Don't worry; the article later explains this better later on.

These long-sought, inaptly named “Population III” stars would have been ginormous balls of hydrogen and helium sculpted from the universe’s primordial gas.

I guess "ginormous" is a scientific term now, probably along with "bajillion" and "metric shit-ton." As in, there were a bajillion ginormous stars in the early Universe, and each one weighed a shit-ton.

Theorists started imagining these first fireballs in the 1970s, hypothesizing that, after short lifetimes, they exploded as supernovas, forging heavier elements and spewing them into the cosmos.

"Fireballs" is misleading, but "exploded" is apt.

That star stuff later gave rise to Population II stars more abundant in heavy elements, then even richer Population I stars like our sun, as well as planets, asteroids, comets and eventually life itself.

Got that? Summary: Pop III came before Pop II which came before Pop I. No idea what they're going to name the fourth generation of stars. Population X, I hope. If this seems backwards, it's because the classification system was developed before people figured out the order of things. Again, the article explains this later.

The early Universe was mostly hydrogen, some helium, a tiny bit (relatively speaking) of lithium, and not much else. It takes nuclear fusion or other processes to create the rest of the elements. This is why we say we're made of star material.

Confirmation is still needed; the team’s paper, posted on the preprint server arxiv.org on December 8, is awaiting peer review at Nature.

Important disclaimer, so you can be That Person at the party when someone gushes about how astronomers found the first star or something.

Because they are so far away and existed so briefly, finding evidence for them has been a challenge.

Remember, we're at the center of an inside-out universe; what's furthest away is oldest. Well. We appear to be at the center, anyway; so does every other point in the Universe.

The rest of the article goes into more depth, and while it's not nearly as paradigm-shattering as, say, detecting life on another world (a subject I've tackled in here before), getting confirmation, or even negation, of this model of the history of star formation would be a step forward in astronomy and cosmology. Thus, the cool factor.

4 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.