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!

about 11 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.

1 Like

Adherennium Plotting something

about 13 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.

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.

June 25, 2020 at 12:30am

#986466

Sense of Wonder

Entry 7 of 8 for "Journalistic Intentions"

[18+], as usual selected at random

7. The only reason I would take up jogging is so that I could fit back into my Wonder Woman costume.

- Whiskersandhersisters

Ever notice that no one gives a shit if a chick wears a Batman costume, but a dude who wears a Wonder Woman outfit would be subject to all kinds of ridicule?

This isn't just because there is, canonically, a Batgirl and a Batwoman, both of whom wear some version of the Batsuit. No, it reflects a deeper problem with gender roles in society.

I'm sure all y'all with liberal arts degrees have already figured this out, but it took me a while.

The problem is this, and I'm using superheroes because I'm familiar with them and because they're inherent to the prompt: female versions of male superheroes are acceptable, while male versions of female superheroes are not. Or, well, I could extend that to "costumed adventurers," because not all comic book heroes are "super." But let's just assume that I'm talking about the unpowered as well as the superpowered here, because superpowers are really irrelevant to the discussion.

So you had, say, Superman, right? And later on, his cousin Kara shows up and she's in the same brightly colored suit but with a skirt (the current incarnation on TV wears pants, but that's not really my point). I've already mentioned the Batchicks. Hulk, and She-Hulk (to be fair, they're very different except for their bright green color). Iron Man, Iron Heart (I'm just glad they didn't call her Fe-Male). Don't get me wrong; there's nothing inherently bad about any of this (though She-Hulk's creation was, shall we say, a bit problematic), but I can't think of even one single instance where it went in the other direction.

That is, take the original canonical female superhero, Wonder Woman, because she's in the prompt. You can't just dress up a guy in the same kind of outfit and call him Wonder Man (yes, I know there is a Wonder Man, but he's an entirely different character and, besides, not even in the same universe). Wonder Woman's origin and entire reason for being is tied up (that's a pun for her magic lasso) in her gender. Black Widow? I mean, you can't even imagine a Black Widower, can you? It doesn't even make sense. Squirrel Girl? I mean, how would you even?

Point is, it seems to be perfectly okay, culturally, for women to take on originally male roles, but it's never been the same for men taking on traditionally female roles. When it does happen, outside of the superhero world, it's seen as some sort of appropriation, or the men involved are seen as somehow less than fully masculine.

I assert that we won't achieve gender parity until this can go in both directions; that is, until it's not seen as "demeaning" for a male character to take on the mantle of one created as a female. Just think about how things would be different if it had been Supergirl first, and then Superman. Or Batwoman first, and then Batman.

There's no logical reason for this; it just reflects the old, entrenched cultural way of thinking, that traditionally male roles are seen as superior to the traditionally female roles. I think that's probably changing, but slowly. "It's okay for a girl to be a tomboy, but never okay for a boy to be a girly-boy."

And no, I'm not going to wade into the quagmire where all of this intersects with issues of sexuality or gender identity.

Comic books are, as I've noted before, a blend of fantasy and science fiction, along with a few other genres thrown in for spice. Fantasy is a really good way to hold up a mirror to our own society, and sometimes, we're not going to like what we see.

So if you ever see a guy jogging down the street in a Wonder Woman costume, try not to leap (over tall buildings in a single bound) to conclusions. Me? I don't think I could pull it off. I don't have the tits for it.

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