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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Brandiwyn🎶

a day ago
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').

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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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

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Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

October 13, 2022 at 12:02am

#1039134

Mask

Another entry for "Journalistic Intentions"

[18+], this one about a trope.

The Woman Wearing the Queenly Mask

The Random Number Generator (peace be unto it) is messing with me again. I just did a "woman in a non-traditional role" entry yesterday.

Fortunately, this one's about a trope in fiction. Unfortunately, it's sometimes difficult to talk about the fictional trope without referencing those works of fiction that purport to be biographical.

Let's start with the TVTropes page. Fair warning: the page suffers from grammar issues. But I think it gets the point across.

For most of mankind's history, leadership and authority are associated with men.

We could start by not calling humanity "mankind."

After all, a leader — especially the supreme ruler of a nation — are expected to be strong (to defend their borders), ambitious (to expand and improve their territory) and aloof (so that they won't be swayed from their long-term goals by a moment of impulse), all of which are often considered masculine qualities.

And yet, some of the greatest rulers in history have been women, and some of the worst have been men. To be fair, there are far more examples of the latter. Perhaps the male ones didn't have to do quite as much to prove themselves capable leaders, due to expectations. Again, though, we're talking about fiction here, and we can write our queens however we like.

So when a woman finds herself in a position of power, expect her subjects to be less than enthused by the idea — a volatile, emotionally-driven, Hysterical Woman in charge of other?

You know who lets emotions get in the way of ruling? Men. Well, anyone, really. We're all human. Society expects us to demonstrate our emotions differently, but in all cases they sneak through sometimes.

While it is possible for this trope to apply to male rulers (if the man in question lacks the traditional masculine qualities, or if the work is set in a Lady Land and the man is forced to be more "feminine" to be accepted), what makes this an Always Female trope is the still commonly held view that leadership is an inherently masculine role, and the point of the trope is that the character suffers emotionally because they are forced to divest themselves of their society's gender norms just to be taken seriously as a monarch.

An ardent feminist once asserted to me that the world would be a better place if all its leaders were women. While I don't really have an argument against that, just to be a troll, I said, "Margaret Thatcher." She responded with, "She doesn't count!"

And now I have an even better counterargument.

The UK Prime Minister isn't, however, a royal; women who are elected (even indirectly, in that case) aren't really part of this trope.

Still, I suspect that any hereditary ruler who isn't a sociopath to begin with has to wear a mask of some sort, regardless of sex or gender identity. Even in an absolute monarchy, rulers are expected to abide by certain... well, rules. And if they don't, if they let sentimentality or passing emotions guide them, well, they tend to get stabbed in the back. Sometimes literally.

I don't think that's any easier for men than it is for women, but I have no way of knowing.

One of the purposes of fiction is aspirational; it doesn't always reflect reality, but rather display how the writer thinks reality should be. And we get used to whatever it is they're portraying. The more shows depict a competent female President, for example, the more likely we are to have one. Not only do we get used to it, but maybe it becomes a bit of an ideal to strive toward for the real person who eventually gets that position.

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