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:

Wordsmitty ✍️

about 20 hours ago
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

a day ago
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

Lilli Munster 🧿 ☕ 🎃

a day ago
In response to "All Out of Louvre"

Have a wonderful time in France. Have you run into Annette in France yet? She's there too!

2 Like

Wordsmitty ✍️

Sep 23, 2024 at 1:14pm
In response to "Bière Snob"

Great to see you got a good shot. And the picture is nice too.

1 Like

Writer_Mike

Sep 22, 2024 at 10:52pm
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

Sep 22, 2024 at 6:44am
In response to "Landmarks"

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

3 Like

Wordsmitty ✍️

Sep 22, 2024 at 3:41am
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

Sep 21, 2024 at 4:44pm
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Go Forth📖

Sep 21, 2024 at 12:51pm
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

December 3, 2020 at 12:01am

#999558

Stuff and Nonsense

For the record, I'm selecting JAFBG prompts using a random number generator, for maximum chaos.

"30-Day Blogging Challenge ON HIATUS" [13+]:
3. National Roof Over Your Head Day!
Tell us about the favorite room in your home.

"JAFBG" [XGC]:
What do you absolutely NOT want for the holidays this year?

I don't have a favorite room in my home.

What I do have is a home. That is, a relatively modest house in a quiet neighborhood that got picked for me by my first wife and her erstwhile business partner. They fell out, we fell out, somehow I kept the house. I decided I liked the house and its location, and so here I've been, absent a few months' worth of travel, for a bit over 25 years.

The last time I refinanced the house, it was on a 15 year mortgage that I managed to pay off early, so it's mine. All mine. MUAHAHAHAHA. No bank, no neighborhood association, just perfectly reasonable city regulations about grass height, snow clearing, not hosting crack parties, and the like.

I don't even have names for all the rooms. I mean, there's the kitchen, the bathrooms, and the bedrooms, one of which is oddly placed downstairs off the utility room that houses the HVAC, water heater , laundry facilities, and a whole lot of stuff. My housemate lives in that bedroom. I mostly keep to the upstairs area.

Also downstairs is a big room that I suppose would be described as a "rec room," because right now it's a wreck. In earlier times, it's been a lounge, a home theater (I still haven't replaced the projector, or the water-damaged sheetrock to which it was once attached), my computer area, a meditation place, and a gaming space, but right now it's kind of everything and I don't use it much. The rec room is covered with stuff right now, mostly belonging to my housemate, including her two guinea pigs who are very cute but kind of a mess. Right off of that is the downstairs bathroom, and it also has a door to the patio. The patio has collected stuff, but only waterproof stuff because the deck above it is porous.

Upstairs is more bedrooms, one of which is mine; the other two are a guest bedroom and my office. All three are chock-full of stuff. There's a bathroom, a kitchen, and a space off the kitchen which I suspect was intended as a living room but now contains a really nice, sturdy dining table, which I mostly just use to sit my laptop on because the office is full of stuff. The bathroom, oddly, doesn't contain much stuff, except the cabinet could use some organizing.

The kitchen has a door that opens up onto the aforementioned deck, which is badly in need of replacement before it collapses, but I've contracted with a guy to do that. Supposedly he'll get to it next year. The replacement won't be porous, so the patio might actually be mostly dry when it rains. The deck has a bunch of stuff on it. The kitchen has a bunch of stuff in it. The dining room is lined with bookshelves containing stuff.

You try living in a place for a quarter of a century, with a changing cast of other characters, and not collect stuff. I don't know; maybe you could do it. I certainly can't. I've been taking some time every day to deal with the stuff, but it's a Sisyphean task. Hell, I don't even know how to dispose of a lot of the stuff.

So I should buy a bigger house, right?

Okay, no. Then I'd have to move all the stuff. Besides, like I said, I like it here; it's in stumbling distance of at least five drinking establishments, depending on what you consider stumbling distance.

And like I said, I don't have a favorite room. Obviously I spend a third of the day in my bedroom, but I don't remember most of that time. The rest of the time I spend sitting on my deck with the laptop if the weather doesn't suck too badly, and that's not a room with a roof over my head, just a patio umbrella. When it's raining too hard, snowing, windy, or cold, I'll sit at the dining room table.

But hey, I'm just glad to own my own home. Which leads me to the other prompt (you knew I had to get to it eventually). My knee-jerk response to "What do you absolutely NOT want for the holidays this year?" is of course Trump Mumps, but that's way too obvious. The actual answer is "anything" because... dammit...

I have enough stuff.

But, you know, there's always room on my new Kindle... and there is that distressingly empty spot in my liquor cabinet...

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