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!

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

a day 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.

November 14, 2019 at 12:04am

#969599

Decisions, Decisions...

PROMPT November 14th

Think back to a moment in your life when you were faced with making a difficult choice. (Which city to move to, which college to attend, what to ask Santa for, etc) How might your life be different if you had made a different choice than the one you did?

Once, long ago, I was dating two women at the same time. Yeah, I know; I was young, shut up. Edith was a petite strawberry blonde who always laughed at my jokes (my primary consideration in a girlfriend) and loved the same kinds of movies I did. Kate, by contrast, was tall, brunette, and enjoyed games (the board and roleplaying kind, not the mind kind). Put them together and you have the perfect woman, but putting them together was the one thing I spent most of my time and energy to prevent.

One day I was humblebragging about this to a friend, who said, "Dude, you have to choose."

"What? Why? I really dig both of them." (We said "dig" at the time.)

"It's just not fair to either of them. Besides, one day they will find out about each other, and then you're well and truly fucked."

I sighed. "Shit. You're right."

"Besides," he went on. "Everyone knows you can't have your Kate and Edith too."

...

Okay, I just made all of that up. Well, most of it. Never let the facts get in the way of a good joke, I always say. Or a bad one. Especially a bad one. Even more especially when you can use the joke to illustrate a point, which is:

Regrets are a bad idea.

Putting aside for the moment the array of scientific evidence to support the idea that one could not have made a different choice given the exact same circumstances, I can't think of even one decision that I made that, had it gone otherwise, would have put me in a better place than I am now. That's because I'm pretty much where I want to be. Oh, life isn't perfect - anyone who tells you their life is perfect is lying worse than I did up there - but I've got a pretty good situation going, even if it's with 0 women instead of 2.

That's probably for the best.

But the question is about how life would be different, not potentially better. Still, my point stands. Besides, if I could have made different choices, I wouldn't be me, and I usually like being me. Or, at least, I prefer it to the alternative.

On the other talon, if I could have made those different choices, the person I would have become would probably prefer that to being me. Unless, of course, he knew what a sweet setup I've got.

Additionally, I can't really think of too many major decisions I've made; life seems to make them for me. At one point, I almost joined the military, but that choice was taken out of my hands on medical grounds. Again - for the best.

So there's a non-answer for everyone, but at least it's some insight into my thought process. Besides, you got to read a funny joke. Right? ... Right??

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