Complex Numbers (Book)

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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/

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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 19, 2023 at 10:10am

#1045084

Revisited: "No Links"

Today's trip down Memory Lane (a street which, for me, is a winding dirt road with numerous potholes) involves what was, apparently, a rare personal update from August of 2009: "No Links"

It's been pointed out to me (though I already knew it) that most of my recent blog entries have been, well, links to funny stuff. People like links to funny stuff, but maybe someone's reading this to actually find out what I'm up to.

I've since expanded my repertoire to add links to serious stuff (that I sometimes make funny), blogging contest responses, and Revisited entries like this one.

Thing is, not much has been going on in Waltzland. My wife's away for a few days, leading me to discover that bare skin sticks to my computer chair.

I want to clarify that this was what's known in comedy circles as a "joke," and is not reflective of reality. However, it was August, so I don't know; maybe I was wearing shorts. And yet, that's the part most of the comments latched on to.

Work is slow, because despite the stock market's optimism, the economy still sucks golf balls through garden hoses.

2009 was, as I recall, the beginning of a bull market that would last over a decade, finally turning bear just last year. But we couldn't have predicted that then, nor could I have predicted when the local real estate market, which kept me able to eat and drink beer, would start cranking back up. Turned out okay for me, though.

It's been raining a lot around here, which means I haven't heard shit about "drought," "water restrictions," or "hot enough for ya?" First person to mention "drought" to me this summer gets a super-soaker in the face.

As I recall, there was a local drought one summer in the 90s or noughties. The details, and the year it happened, escape me, but I do recall that after a sweltering summer with constant reminders to take shorter showers, let your lawn die, and not flush the toilet until it became absolutely necessary, and other exhortations to please, for the love of god, conserve what little water we have left in the reservoir... after all that, the local water authority complained about having lost money that year, and thus wanted to institute a massive rate increase.

This led to me swearing to never conserve water again, because the only reason to do so would be so that they could raise rates afterward.

Well, we haven't had a significant drought since, and I do try to conserve water, so, so much for that.

I've been going to a local science fiction & fantasy book club for the past few months. We meet once a month to discuss the assigned book, plus whatever other books we've been reading, and to complain about crappy science fiction movies (that is, this year, every one except Watchmen and Star Trek. Shut up, Stik.)

That was a fun club. I don't remember what other movies came out in those genres that year, and can't be arsed to look it up, so I also can't remember what I'd been arguing with Stik about. (Stik, your memory is much better than mine, so feel free to remind me.)

I think I'm the only married person there. Surprisingly enough, at the last meeting, women outnumbered men (and we didn't end up discussing Twilight).

Yes, that was a sexist comment, I know. After that, no one invited me to be a public speaker. Oh, wait, no one invited me to do that before the comment, either.

Oh, and I went to New York City over the weekend. Somehow never got around to mentioning that. I've been there three times this year, now, so it almost seems routine. Got some good pictures, though.

Three times might be my limit. Usually, I visit once or twice. During the... you know... that dropped to zero for a couple of years.

Which reminds me - I finally broke down (literally broke) and bought a Nikon digital SLR. It fucking ROCKS.

That was a good camera—for the time. Haven't used it in years. Smartphone technology quickly left its picture quality in the dust. As I have no intention of getting back into professional photography, or even serious amateuring, the built-in camera is good enough for me, and it's way easier to carry around and back up.

3 Like • Comment • View 2 comments

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