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').

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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.

May 27, 2021 at 12:03am

#1010837

And The First Shall Be Last

PROMPT May 27th

Write about your first _______. (You fill in the blank. Ex: first car, first job, first crush, first week at college, etc)

It's not like I'd never had a taste of an adult beverage before.

My parents operated on the theory that if it's not seen as The Forbidden Fruit, I wouldn't be as tempted to overdo it when it was finally legal to drink it. So they let me have sips here and there, mostly of wine or beer.

That worked out well.

To be fair, it probably would have been worse if they'd completely forbidden it. Or if my first beer hadn't been such a disastrous experience.

Like I said, I knew what beer tasted like, but I count my "first beer" as the one I chose for myself, the first one I didn't get parental permission for, the first one I drank in its entirety as the gods intended.

I was 16, and it was a boat party. The other kids there were around my age. Some had their drivers' licenses, like me. Some did not. The boat's owner made it clear that if we drank, we weren't driving, period, end of story, give him your keys. He was still breaking the law, of course, just by having us there, but he wasn't about to be responsible for drunk kids driving on the roads. I respected that. Still do, actually, though I wouldn't have had the kids on my boat to begin with. If I had a boat. If I knew any kids.

And just to be clear, it was a big boat. I wouldn't call it a yacht; nothing about it was luxurious, but it was a nice roomy houseboat with plenty of places for drunk teens to sleep it off. More to the point, it was too big to sway much in the dinky little waves of the estuary. This is important, because the only thing worse than someone unused to alcohol getting sick, it's someone unused to alcohol getting seasick.

So that's where I had my first beer.

Well, I called it beer at the time. I'm embarrassed to admit that the name on the can was: Red White & Blue.

Kids these days will never know the glory of the RWB. This is probably a good thing. No, this is definitely a good thing. Objectively, there is little difference between RWB and water. But, at 16, what do you care? It's beer. It's illegal. It's edgy. Nowadays, if that piss were still around, one can of it wouldn't even register to me as alcoholic, assuming you could get me to drink it in the first place, which is a really bad assumption.

In any case, they don't make it anymore.

But after that one can, there I was, hanging off the side of this giant houseboat, emptying the contents of my stomach into the murky waters of the calm estuary.

Yes, I swore off beer after that until I got to college, where peer pressure forced me to drink nearly-as-bad examples of the brewing "art." It wasn't until years later that I discovered the wonders of craft beer.

And yet, every once in a while, I remember that first beer.

It was great.

Oh, hey, some of you were wondering about one of my goals from yesterday: "Maybe write fiction again?" Well, I got to thinking about it a few hours ago, and decided there's no time like the present. So I wrote a story for "Invalid Item"

. Here it is:

STATIC

The Trolley Problem

(18+)
What's the actual solution?
#2251176 by Robert Waltz

No promises that I'll write more anytime soon. But there it is.

9 Like • Comment • View 4 comments

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