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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Turkey DrumStik

about 7 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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.

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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

November 8, 2018 at 1:45am

#945138

What I'm Doing Here

The more I write, the more I want to write.

Honestly, I thought it would be the other way around. I expected that by committing to blogging again after so many years, it would burn me out, run me out of ideas. But the opposite has happened.

I should have known better, really. When I'm stuck and I want to write, I do what I call a core dump (because I'm a Unix geek from way back) - take a blank file and just start typing, stream of consciousness stuff, nothing I'd ever show anyone else. It's just to get my thoughts out there instead of circling around in my head, freeing my mind for the task or goal I've set. I don't even worry too much about typos in a core dump, which should tell you something; I don't like to display misspellings and grammar problems in what I write. Oh, I know they get through often enough, but normally I avoid them like the outdoors. Point is, a core dump is a very different thing from a blog entry, but they do have one thing in common: after getting my thoughts out, new ones inevitably pop up.

Naturally, I haven't done anything about this yet.

The main difference between a core dump and a blog entry is audience. Although I write both primarily for myself, with a core dump, I know that no one will see it (or at least I hope not). With something like this, there's always the knowledge in the back of my mind that someone might actually read it. Maybe even someone I know nothing about. Will I offend someone? Am I revealing too much of myself? Not enough? Will they skim the boring parts, like I do when I read someone else's writing?

The blogs I follow offsite are done by people with deep knowledge of a particular field, notably astronomy and biology. I dislike watching videos for the most part, because it's harder to skim the boring parts. I shun podcasts as well; hell, I've never heard a single podcast. I read, and therefore, I write.

I also avoid Twatter and Failbook. The latter has turned into something reminiscent of MySpace pages back in the noughties, with shit blinking and moving around; it's annoying. And the former is like arguing with bumper stickers. The first I heard of Tweeter was when a friend of mine told me that some guy had rigged his office chair to Twit every time he farted, and nothing I've heard about that platform since then has led me to believe that it's gotten any classier. Yeah, yeah, I know there's an art to writing with a limited number of characters; it's just that, usually, I need more depth.

And that's my problem when it comes to putting my own thoughts out there: I lack depth of knowledge on any subject, having spent my life preferring to know a little bit about a lot of things rather than a lot about one thing. The only exception is civil engineering, but that was my career and I don't really want to write about the intricacies of parking lot design.

My approach does have its advantages, though; as a writer, I like to make connections between unrelated topics. "Write what you know" doesn't mean to limit yourself to stuff you already know; it's an exhortation to broaden your own pool of knowledge. Sure, there are some topics that attract me more than others, but I try not to miss an opportunity to increase my understanding of something. I've said this before, but there's no such thing as useless knowledge.

And my hope is that I make people think - and laugh.

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