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 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 1, 2023 at 10:24am

#1042436

Revisited: "Someone's Birthday"

Well, here it is: my first blog post of 2023.

I usually post just after midnight, but obviously I was too drunk to be coherent, so I waited until I was hung over. It may be Amateur Night, but us drinking professionals enjoy it too. It's just that I celebrated at home so I wouldn't have to deal with the amateurs, or get judged by an Uber driver.

I could use this post to look forward to the new year, but that's trite. Or I could make my usual jokes about how you've already failed all of your New Year's Resolutions, but that's even triter; no, I think I'll save that for this week's Comedy newsletter. Alternatively, I could take advantage of the flipping of the calendar to announce a major change in posting format, or a new blog contest that I'll run, but neither of those things are going to happen. Well, the blog contest might happen, but it won't be dependent on some arbitrary odometer change. (I'm toying with the idea of a weekly blogging contest, where I post a prompt and you have six days to take it where it leads you. We'll see.)

But no. If it wasn't Sunday, I'd pull a random article from my still-lengthy queue and rant about it, as per usual. But it is Sunday, and I've been using Sundays to pull the levers on the Wayback Machine, so that's what you get today. Today's blast from the past is from May 10, 2019: "Someone's Birthday"

This is a short one and a response to a 30DBC prompt (I kinda miss that activity, though not enough to jump in and work on it), and, as the title suggests, it celebrates the birthday of Sum1's In Kalispell Montana

.

Sum1's In Kalispell Montana can be summed up with one word: mushroom. No, wait; that's not it. Toadstool? Well. Some sort of fun guy anyway.

Since I posted this, the author in question changed his username. Oddly, the old links still work. I thought they broke when someone changes their username, but apparently not.

I'm not sure whether this was the first time I made the "fungi" pun in the blog. Probably not; I've been spouting variants of it since high school. It certainly wasn't the last time. I know, I know; it's a morel failing on my part.

After all, Sum1's In Kalispell Montana is the curator of "Smile! (Groan?) You Know You Love These!" [13+], which does almost as much to spread laughter as my own comedy does.

And this is how my sense of time sucks: I didn't realize he'd been posting those for so long. It's a regular part of my daily routine to read them.

I don't remember when I first met Sum1's In Kalispell Montana. It was probably in the super-secret Moderators forum, which the rest of you can't know about. I know he hasn't been around as long as I have, so really, he's just a kid.

When I wrote that entry, I hadn't met Jim in person. Since then, I've seen him... let's see... four times? Once at dinner with 🌕 HuntersMoon when he was in our area; once on his own turf in Ill-annoy; once when we took a day trip to Newport News for some whiskey; and once when he gave me an excellent bottle of moonshine (and I reciprocated with a bottle of Belizean hot sauce). He gets around because of work. I get around because I like to travel.

So anyway, to be clear, today isn't his birthday; I just landed on that post at random, as per my usual method for finding old blog posts. But, like many people on WDC, I consider Jim a friend and hope we can get together again sometime. After all, I still owe him booze.

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