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:

Elycia Lee ☮

about 9 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 22 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
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

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

January 12, 2020 at 12:30am

#973200

Tougher Than the Rest

PROMPT January 12th

Describe a time when you exhibited bravery.

Well, one time I touched a cat's belly fur...

Or... no, I shouldn't talk about it.

Okay, fine; I've been drinking, so I'll talk about it.

Long, long ago, when I was young and stupid (as opposed to now, when I am old and stupid), I was banging this married chick. She lived a couple hours away, right on the edge of the state, and sometimes I'd go over there on Friday nights and stay the weekend. The alternative was staying home and dealing with my first ex-wife, who hadn't yet moved out.

The woman's husband, a long-distance trucker, was never home.

One time I went over there, on invitation, and he was home.

So I played it cool. Just friends. Hanging out. No big deal.

Until he brought out the guns.

"Hey, Bob, let's go target shootin' in the woods."

Gulp.

Oh well. I'd recently been in bed with two hot redheads (the wife in question was one of them), so I figured this was as good a time as any to slip the bonds of this mortal coil. I just hoped he would make it quick. So I agreed, and he handed me one of the rifles.

A bit more background: as I've noted here before, I spent my childhood in rural Virginia. Rifles and shotguns were just tools to me - like tractors or scythes, things with a purpose that also happened to be dangerous, so my dad had instilled in me safety procedures for the various farm implements, including guns. Some of these procedures actually stuck. There wasn't any of the modern-day abject fear of the weapons themselves in me; I'd been shooting rifles, shotguns and even pistols since I was old enough to stay upright after the recoil.

Fear of jealous husbands, now, that's another story. I'd always said that I wanted to die by being shot in the back by one whilst trying to escape out a window, but what I meant was it should happen when I was 100 years old.

Not 30.

Besides, the guns, as it turned out, were old-fashioned single-shot muzzle-loaders. I'd never fired one, and I was curious. As I recall - this was, of course, some time ago - you stood the weapon upright, packed in a charge of black powder in a little sack, and then packed the lead ball on top of that. After, you didn't want to point the gun down, lest the bullet fall out. All of this, The Husband explained to me as we stood out back of their house, a paper target tacked to a tree just over the property line on National Park land (this was probably illegal, but that was the absolute least of my worries at the time).

Spoiler alert: he didn't shoot me. In fact, I think that either he believed that I was just some random friend she'd found on the then-nascent internet, or - more likely - he knew that his job kept him away from home for extended periods, and he didn't begrudge his wife the occasional dalliance.

(I should further note, here, that I was between wives at the time. My first wife had just asked for a divorce, harsh things were said, and she finished with "I hope you get what you deserve." She'd said it in a way that implied that she thought I deserved getting my nuts stuck in a paper shredder. So we officially separated. It was that weekend that I found myself between two hot redheads. Later, after we'd divorced and gotten on speaking terms again, we had a good laugh about that.)

So, in retrospect, I think The Husband just wanted to see if the dude his wife was banging had the stones to go out back with a larger guy who was holding a gun. Whatever the reason, I learned my lesson. No more married chicks for me. Well, except for the one other time, but my excuse there is she was married to me.

Oh, and for the record? I was a much better shot.

Some girls they want a handsome Dan
Or some good-lookin' Joe
On their arm some girls like a sweet-talkin' Romeo
Well 'round here baby
I learned you get what you can get
So if you're rough enough for love
Honey I'm tougher than the rest

6 Like • Comment • View 9 comments

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