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!

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').

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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.

July 23, 2019 at 12:32am

#963033

Phobos

Write about a fear you experienced as a child that you have since overcome.

Before I do that, there's something that's been bugging me for a while.

Now, I admit I'm not the most emotionally aware person in the world, so maybe someone can explain this to me.

We conflate hate and fear, and I don't understand why.

I know that some schools of thought (mostly very New-Age-y) hold that all human emotion can be categorized as, at base, either love or fear. Under "love" in this philosophy we have, I suppose, things like affection, camaraderie, comfort, whatever - those emotions we consider "positive." Under "fear," by contrast, would be things like greed, jealousy and hatred, the "negative" ones.

I once had an epiphany that since fear is an emotional response to a real or perceived threat to something that we love (including our lives), that would mean love is the basic emotion. I suppose you could turn that on its head and declare that fear is the only real emotion. More likely, you can dismiss the whole philosophy as the bullshit that most New Age stuff is.

But that's irrelevant; I'm talking about hate and fear here. Like I said, we conflate it: hatred of something usually gets the -phobia suffix added on, indicating fear. However, the Venn diagram of "hate" and "fear" seems to me to have overlap, but it's not a perfect circle. For example, just to use a common fear, maybe you're one of those weird people who goes outside and you're afraid of bears. This is logical; a bear can fuck up your day. Still, this doesn't mean you hate bears; it just means you don't want to be eaten by one. Bears are, apart from the whole "outweigh me by a thousand pounds and possess sharp teeth and claws" thing, pretty damn cool. Of course, it's possible you both hate and fear them, but it's not required.

Likewise, maybe you hate, I dunno, PETA. This, too, is understandable; they're a bunch of extremist hypocrites (personally, I think they're being funded by the soybean industry as a way to increase demand for their product, but I have no proof of this). But there's certainly nothing to fear about them. What are they going to do, bleed on you?

Hate and fear are not the same thing. So why the "-phobia?"

The best I can come up with is that it entered the public consciousness as a kind of social engineering. A lot of people (okay, men) find it socially acceptable to hold hatred in their hearts, but if you suggest that they're actually cowards, they feel shame about that. If this is true, it needs to stop; the goal should be to get people more in touch with and understanding of their own emotions, not leverage atavistic impulses to further your own aims.

But I don't know if that's true. I'd really like to hear others' take on it.

When I was a kid, like all kids, I was afraid of a lot of things, mostly because I didn't understand them. This, I think, is the sort of thing that fosters fear: ignorance. I don't see ignorance in itself as a bad thing; it's correctable. It's the people who refuse to learn who deserve scorn, not the generally ignorant. Everyone is ignorant about some things and enlightened about others.

To address the prompt, then, I guess I'll have to admit that when I was a kid, thanks to movies, TV, and the science fiction books I loved to read, I was sure that space aliens existed and wanted to abduct me. This, naturally, freaked me out, as if the constant threat of nuclear annihilation wasn't enough. Other kids maybe feared the monster under the bed, but not me. It's not that I didn't think there was a monster under my bed; it's that the monster would have been abducted by aliens, too, so we had common ground to bond over.

Why more people don't buy kids beds without space underneath them, I simply don't understand. Maybe it's so the monster stays there and doesn't interrupt the parents while they're boning.

Anyway, point is, I got over it. For a while there, as a kid, I had certain rituals I did to ward off the aliens. As an example, I just knew that as long as I had my back against something, they couldn't beam me up (fears have never been known for making a lot of logical sense). I could never sleep on my back, though, so instead of hugging a pillow or a bear like other kids, I kept my back against one.

It must have worked, because I was never abducted or replaced by aliens.

Or, at least, I wouldn't admit it if I had been, fellow humans.

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