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 3 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!

a day 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

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.

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

January 1, 2019 at 12:59am

#948587

So it Begins

What is your opinion of New Year’s Resolutions? Do you make them? Do you keep them?

I think I've made my opinion quite clear.

It's a very human desire, I think, to be able to start over, to forget the mistakes and failures of the past and, in the words of Hester Prynne, "begin all anew." Or something like that. I haven't read The Scarlet Letter since high school. That quote is about the only thing I remember from it, except for the idea that we can't really start over, that our mistakes follow us until we die, and sometimes beyond.

Still, I'm not against self-improvement. I just tend to do it on a different time frame. My birthday, maybe, which is in February. Or, in the case of this - I mean, last - year, the solstice.

That's when I made a commitment to myself to work on my health issues. It's been nearly five years since my heart attack, and I've had some success eating better and exercising, but it's been sporadic.

I really, really need to lose weight. Not just because fatties get mocked, and not just because I don't fit into airplane seats anymore - no one fits into airplane seats anymore, except kids, and we don't need more of them on airplanes - but because I want to try to live a little longer and not get diabetes.

It's actually a minor miracle that I'm not diabetic as it is.

Anyway, so it wasn't a New Years resolution, but it was a solstice decision. I've been monitoring my calories and keeping them low, and walking more. I also didn't drink any booze. It's been working. I've lost weight. I did drink a glass of wine tonight; it is, after all, New Year's Eve.

The problem is, the solstice is very close to New Year's. This is a problem because now, everyone else is trying to do the same thing I am, and if there's anything I hate, it's following trends.

Worst part about it is, walking will only sustain me for a limited time. Eventually, if I manage to keep this up (absolutely unlikely), I'll need to go back to the gym. In January. When everyfuckingbody else is also doing the same thing.

That's why I usually wait until my birthday to make these decisions. By then, everyone else has failed, and I practically have the gym to myself.

Anyway, my hope is that this will also help with the depression. It has in the past, but then I fail, and I feel even worse because I've failed. I'll fail again, and I'll feel bad again. It's the circle of life. It will end when I'm dead. I'm just hoping that will be later rather than sooner.

Maybe writing this here will help keep me honest. I doubt it, but it's worth a try.

12 Like • Comment • View 8 comments

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