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 19, 2018 at 1:23am

#945840

Writer's Block

As you probably know, I'm not doing NaNoWriMo this year.

I've had three successful NaNos, meaning I met my 50,000 word goal and got out something that passes for a coherent narrative each time, but I just wasn't feeling it this year.

So, what does it take for me to "feel it?"

Let's take as a given that I want to get more writing done. I mean, I think I'm pretty good at it, and there aren't that many things I'm good at, so it strikes me as something I should want to do. But, as I've explained before, I like to do a lot of things, not just concentrate on one activity (not even video games or drinking, both of which are activities that don't require much creativity).

One thing I've learned from my NaNo experiences: writing, really, isn't about inspiration or motivation; it's about work. It's about getting the words out there, outlining, planning, coming up with characters and situations, and - my personal monster - editing.

So, first, I'd have to get past my aversion to work. I like the easy paths. I may be an adequate writer, but writing is hard. Not physically demanding, at least, but mentally challenging - at least if I'm doing it right, and I demand of myself that I do it right. It's why I don't brew my own beer. Beer is one of my favorite things in the entire universe, but how could I possibly brew a superior beer when there are over 6000 breweries in the US alone, many of which create a delicious amber nectar that I couldn't even hope to approach, let alone surpass? So I'm content to drink those, in the same way that I enjoy reading Brandon Sanderson or Jim Butcher and going, "Okay, there's no way I can ever be that good, so why bother?"

The second thing I need is ideas. Not just one idea. I never do anything for just one reason; that would be inefficient. I think my best work combines two or more ideas and plays them off each other. But I'm not a very creative person by nature, so even coming up with one idea is like hiking up a mountain.

And finally, there's the discipline to sit down and actually do the work, ideally every day. I know I can, because I have, but thinking about doing it again makes me itchy. The worst thing is, I don't know whether I'm more afraid of failure or success. Failure sucks, and success is great, but if there's one lesson that I've truly internalized in life, it's that you can't bring anything new into your life without making room for it by releasing what's already there.

That may be the most difficult part for me: I'm pretty much where I wanted to be in life. But it's a giant Jenga tower: at any time, something could bring it all crashing down if I remove it, but I'm not sure which block will cause the catastrophe. So I keep everything as close to the way it is as I possibly can.

Hell. Probably I need to see a shrink again, although the last one wasn't all that helpful with his "you know, most guys would give their left nut to be where you are right now." Yeah, thanks, I know that; but that doesn't mean there's no room for improvement.

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