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 11, 2023 at 11:13am

#1055576

Hindsight

No external link today, just some personal reflections on 19 years of Writing.Com.

The problem with having an account creation anniversary today is twofold:

One, it falls close on the heels of WDC's Birthday Week celebration. On this site, that's rather like being born just after Christmas in the US: everyone's burned out on celebratory cheer, and ready to go back to being their usual grumpy selves. Or, possibly, gearing up for NaNoWriMo (shameless plug for "October Novel Prep Challenge"

[13+], which is taking signups and looking for more Contest Round judges).

And two, it coincides with another anniversary.

That other anniversary was very fresh in everyone's minds back in 2004, when I signed up here. This year, I haven't seen any mention of it at all, and I follow the news cycle pretty damn well for someone who shuns popular social media (RSS is still around, and it's easy to set up your feed the way you want it; it's just not as easy as getting it spoon-fed by the algorithms on Xitter and the like).

But it wasn't supposed to be September 11; it was supposed to be the 10th. As I recall, I had some problems getting registered way back then, and it was only about 2am on a Saturday that it finally worked. That's also the reason for the annoying 02 at the end of my username; earlier attempts to register as just cathartes failed, but locked out that option. I keep meaning to change my username, but after 19 years, it seems like that would cause more problems than it would fix.

I've told that story before, but who could read all the entries here? I sure haven't.

For the curious, I'm pretty sure this was the first thing I posted in my port: "Ghost Poem #1"

[ASR] Considering my evolution since then, it's strange that my first bit was a poem, and a serious one at that. I still do them occasionally, but I'm more tuned to comedy, these days. At least I'm not embarrassed by that poem, which is older even than my account. Not embarrassed much, anyway.

I barely remember last week, let alone 19 years ago, and I don't know a way to view one's portfolio in chronological order. So I could be wrong about that being my first item. Doesn't matter; close enough, as it was the same day I joined. That, of course, made me a Registered Author. I don't remember when I became Preferred. I also don't remember the exact date I got the blue case, but it was sometime in August of 2006... probably. Like I said, my memory sucks. I still think of myself as one of the newer moderators, when that's objectively not the case (pun intended).

And I started this blog the following New Year's Day. I took a years-long hiatus from it, but decided to keep going with the same item rather than start a new one, mostly because come on, the name is awesome.

Unfortunately, it's now almost full. Around 95% by byte size, and 82% by number of entries, not counting this one. I doubt it'll last another year at the rate I post (daily, relatively long entries), so this might be my last anniversary retrospective here. I won't delete entries, and it's unclear to me whether I'd get more space in the blog if I switched to a Premium Plus membership.

I'll design that bridge when I get to the chasm. Right now, just let me end by thanking everyone who left me anniversary notes and done Anniversary Reviews, including one of that ancient poem of mine I linked above. This is not me begging for more, only acknowledging those that have done these things. It's been a great community, and I've made a lot of friends I never would have otherwise met, both online and in person. You know who you are. While I doubt I'll be around for another 19 years, as I'm pretty sure I'm not an immortal, I'm not planning on going anywhere anytime soon. So you're stuck with me... unless, of course, you put me on ignore.

8 Like • Comment • View 2 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.