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:

Write_Mikey_Write!

about 21 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 23 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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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