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 3 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 5 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.

September 15, 2020 at 12:20am

#993382

It's an Ill Wind

Wait, September's halfway over already?

PROMPT September 15th

Have you picked up any new hobbies or interests since the start of the COVID-19 pandemic in March?

Short answer: No.

Long answer: Nope.

Rambling answer:

This period is notable for having removed, not added, things to my life. These removals include, but are not limited to:

Travel

Haircuts

Gym workouts

Movies (but see below)

Massages

Barstools (as per the entry from 12 September)

Visits with friends

A few of the hobbies/interests I had before the beginning of 2020 continue, though. The most recent one is Duolingo, started last August, and I suppose I can credit the pandemic for my not missing a day of French lessons in over a year. I've learned quite a bit, but still consider myself a novice. J'apprends le français lentement, et j'espère continuer.

Obviously, I'm still writing. And watching shows and movies online, and playing the occasional video game. Oh, and drinking, of course -- the only thing I can say has increased in frequency during this shitstorm of a year, as detailed in an earlier entry.

Movies -- other than streamed ones -- are kind of a sore point for me, as with travel. The closest thing to a New Year's resolution I made was I decided that 2020 was going to be the year I was to branch out and see more, and more varied, movies in the theater, because there's one convenient to my house that also serves beer. And I started out doing just that, but then... well, you know. The theater itself was shuttered completely for a good five months, and has only recently reopened, with severe restrictions for safety. I've been going about once a week since it reopened.

The moral of this story is, as always, don't make resolutions. Even if it's something you like to do. Especially if it's something you like to do. I'm not saying that a global pandemic hit, sickening millions and killing hundreds of thousands of people, just to fuck with my weekly cinema visits, but it sure feels that way sometimes.

I've also mentioned before that I didn't drive for six months. As in, I didn't even start my car. This, predictably, led to a service call. But on Sunday, I picked a random destination (I mean that literally; it was a randomly chosen spot within a 30-mile radius) and drove there and back. Not that I didn't go anywhere for six months, but between walking and Uber, I didn't really need to drive. Even doctor appointments are within walking distance. One time I went to a dentist that was really too far away for me to walk, but again, that's where rideshare comes in. Besides, there are breweries near the dentist, and they were open.

Oh, if you're still with me, you're probably wondering about groceries if I didn't drive. My preferred grocery store is near the theater, definitely walkable -- but not on the return trip while schlepping cases of Crack Zero and bags full of groceries. But I've been getting groceries delivered since before the pandemic, for various reasons, and that's continued, too.

One good thing to come out of all of this: used to be I'd get the occasional craving for fast food, and run out to indulge it. After six months without Taco Bell, though, I might have -- might have -- kicked that habit for good. I certainly have other unhealthy habits, but that one always bugged me.

My father used to say, "It's an ill wind that nobody blows good," but he was referring to the oboe. I think the point of the original saying is that something good can come out of even the worst of times. I guess he was familiar with the original because he survived the Great Depression, a world war, and the last major pandemic. Yes, the 1918 one. He was just an infant then, but still. (Obviously he's not around anymore, in case you didn't know that from earlier entries.)

So, no, I haven't picked up anything new during this. I'm just biding my time until I can travel again.

9 Like • Comment • View 7 comments

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