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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Write_Mikey_Write!

about 12 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.

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Adherennium Plotting something

about 14 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.

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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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 8, 2020 at 12:27am

#983049

Value Judgments

"The Ultimate List of 400 Personal Values?" I'd bet I can think of at least one that's not on the list.

PROMPT May 8th

Take a look at this list of values: https://liveboldandbloom.com/wp-content/uploads/2019/01/400-personal-values-list...

Pick your top ten values and rank them based on how important they are to you. Then, write about the values you chose and if any have changed throughout your life.

I'm not a consistent person (yes, consistency is on the list). So if I were doing this prompt yesterday, or two hours ago, the result would probably be different.

Without context, I can't tell if these are meant to be values we look for in others, or strive for in ourselves. To me, that's what personal values are -- things to strive for, not fixed personality traits. But in looking for them in others, we see how well the person wears said values. So I'm approaching this as an exercise in what's important to me, things that I either work towards or want to work towards.

Also, "extroversion?" Seriously? Like that's something one can strive for? At least it also includes "introversion."

So to get this out of the way, Waltz's Top Ten Values, As Of The Early Morning of May 8, 2020:

10. Comfort
9. Fairness
8. Wittiness
7. Independence
6. Cleverness
5. Efficiency
4. Learning
3. Wealth
2. Humor

And the #1 value from the list is (drumroll...)

1. Reason

Yes, I'm aware that some of those are considered shallow. So be it. I'm not going to pretend to be something I'm not -- well, not unless it's something I want to be, and then I'll pretend the fuck out of it until I become it.

I'm also aware that 8, 6, and 2 are basically restatements of the same thing. Doesn't matter. Comedy is that important to me. Though "cleverness" extends beyond comedy into being able to figure things out. Before you go tearing me up for not being clever, I didn't say I was clever; I said the concept is important to me.

I didn't always realize the importance of comedy in my life. I think most people are like that, at first, not being able to articulate what we value. One day, it struck me that humor -- having a sense of humor, being funny, being perceived as funny -- is actually one of my main motivations in life. I wish I were better at it. Sometimes, I think I'm brilliant. Other times, not so much. Doesn't matter; what matters is that I try. Not only is it important to me to make jokes, but to spread mirth, and to be able to laugh at others' humor.

"Wealth" seems materialistic, I know, but it's a prerequisite for "comfort" and "independence," at least for me. A means to an end, not an end in itself.

As for #1, well, anyone who reads this blog should know that I value reason. Not exclusively, of course; part of "reason" when applied to humans is knowing that they're largely unreasonable, emotional, irrational.

Speaking of reason, the list claims 400 values. I counted the first column: 50. There are eight columns. 50*8=400. Math isn't hard. But one of the items, "knowledgeableness" (wtf) is almost German in its compoundedness. The word is so long that it takes up two lines, and that column isn't any taller than the others. I can't be arsed to count to 400, but that particular column does, indeed, contain only 49 values. Therefore, the title is misleading and whoever put that together should feel bad. Not just for not knowing how to count, but... seriously... "knowledgeableness?"

My browser spell checker doesn't even recognize the word. And yet I still like it better than "being-ness."

In conclusion, I identify with a lot more of those values, but this exercise is Top Ten so that's what I stuck with. Empathy is one example; I've noted before that it's something I want to work on. It's... not going well.

There are also some -- I'm looking at you, being-ness -- that are the polar opposite of what I value. Conformity. Fashion. Extroversion. Piety. And I'm amused that "adequacy" is on there. "Oh, yes, I strive for adequacy. One might say I even have delusions of adequacy."

And what in the liquid hell is "buoyancy?"

Absurdity. Absurdity isn't on the list. I propose it for the Missing Value to make it an even 400. Hell, it might even make my Top 10 next time I think about it. If I ever do. It'll be more efficient if I don't.

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