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 6 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 8 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 4, 2022 at 3:06am

#1024136

Judge, Mental

2022 continues to live down to all my expectations thus far. Yesterday morning, we got a few inches of ugly, dense, watery sn*w which brought down branches, leaves, trees, and a nearby transformer (the electric kind, not the Michael Bay kind, though I did get to hear it explode). And my home generator picked yesterday to go on strike for higher wages and better working conditions. To be fair, any wage would be higher that what I'm paying it now, but come on, you only have to work like twice a year; get over yourself.

Thus the late blog entry; electricity just returned, naturally, announcing its homecoming with great fanfare (literally; I'd neglected to turn off the ceiling fan after the power cut out) about five minutes after I'd drifted off to a shivering, restless sleep. Oh, did I mention it's 20F out there? It's 20F out there, and everything is covered in formerly mushy, now icy, sn*w. If the power hadn't popped back on in the middle of the night, they'd have had to chip my corpsicle out of the solid block of ice that had once been a house.

Look, I live in Virginia. I expect this kind of shit at least once per winter. It doesn't mean I have to like it.

Anyway, though late it may be, I can now do today's rant for "JAFBG"

[XGC], which is completely unrelated to crappy winter weather, the robot uprising (which is how I categorize my generator refusing to work), or me not getting any decent sleep.

Fess up. Everyone's a little bit judgmental. What is the thing you're quickest to judge someone about?

I might have told this story before, but whatever.

One time, several years ago, I was drinking at a dive in some small town in South Dakota because it was within stumbling distance of that night's hotel. It wasn't bad as dives go; clean, at least, and the clientele didn't look like Klingons after a hard day's battle. There were a few taps, some of which were even some of the better-known craft brews, so I sat at the bar and ordered a Fat Tire and started going through that day's photos on my phone or some shit.

After a couple, I started feeling pretty good despite being in a shitty bar in a shitty town in a shitty state (okay, that's not fair; South Dakota is actually rather nice from what I've seen). This lanky guy comes in, straddles the seat next to the one next to me, and catches the bartender's attention.

"What'll it be?" sez the barkeep, or words to that effect.

"A Bud Light and a water."

And I was just drunk enough to say, out loud, "So, two waters."

The bartender ignored me, and, fortunately, the guy who ordered two waters just kinda snorted, and then ignored me. As opposed to punching me in the face, which is an occupational hazard of drinking at a dive bar and disrespecting someone's chosen libation. Or looking at them funny. Or looking at their girlfriend. Or being from out of town. Or just being there.

The point is, yes, I instantly judge you based on your beer selection.

It's not fair, and I know it, but I'm not perfect (especially when I've had a couple). It's just that I used to drink that swill, too, but then I tasted Real Beer™ and never once looked back. Well, okay, maybe once or twice, if it was free at a party or whatever, just to confirm that I still had a functioning tongue. But if that dive bar had offered nothing but fake American watered-down rice-ass beer, I would have just asked for the water. Or, more likely, a gin and tonic, because I'm not quite as snobby about those.

Once I get over the initial judgement, though, reason sets in. Maybe they don't have a lot of money, and still want to pretend to drink beer. Maybe their palate is about as complex as a doorstop. Maybe... shudder... maybe they actually like it better.

And really, I don't want to shame anyone for drinking what they like. After all, I don't judge people who simply don't like beer at all, or who don't drink for whatever reason. It's just when someone has a choice between Crap Lite and, well, pretty much anything else, and chooses the Crap Lite, my inner judge, jury, and executioner kick in. Well, maybe not the executioner. Like I said, I get over it pretty quickly.

Also, face tattoos. But mostly it's the beer thing.

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