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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Turkey DrumStik

about 5 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

December 21, 2018 at 12:32am

#947902

Values

Every once in a while, I get pushed something like this:

https://getpocket.com/explore/item/a-list-of-8-core-values-i-live-by

Coming up with one's own core values is certainly preferable to having them dictated by something outside yourself. Taking one from that list, let's use the first one, "authenticity," for example:

I don't think that's something I could adopt. Perhaps that makes me a bad person; I don't know. But the author explains it thus: "Be the same person at every occasion in life. Don’t act differently in front of your parents, friends, co-workers, in-laws, and strangers. Stay your true self. And never be afraid of other people’s judgments."

That's not me. My "true self" is a bit of a chameleon. I'm going to act differently in front of friends and strangers (I no longer have anyone in those other categories in my life).

Now that I think of it, this may be one reason I'm lousy at parties. I don't know who to be at any given moment. I feel the others sizing me up: "He's going for the cheese dip again, like he needs it." Well, I don't need it, but I enjoy it. How am I supposed to explain to people that I've never met that the joy I get from food is more important to me than being fit, or even my health?

I guess I'm doing that now, trying to explain something to people I've never met.

It wasn't always this way. When I was younger, I had more self-control. With the future ahead of me, I figured I could try on different personas, find one that fits.

Nothing ever did, so I essentially gave up. And now I don't know how to start giving a shit again. I guess it's just not that important to me.

What is important to me? Solitude - not all the time, but good chunks of it; I suppose this is helpful for a writer. Learning stuff - I feel good when I learn something new, even if it challenges what I thought I already knew. Comfort - also not all the time, but having someplace to which to retreat (I suppose this is related to solitude). Freedom - that is, being able to make my own choices without those choices affecting other people.

There's probably more, but those don't strike me as lofty ideals at all.

I read somewhere recently that who you are is more about what you do than about what you believe. Like, say you believe that it's important to stop climate change - but you still drive a low-mpg car and make unnecessary trips in it. Or if you believe in the fundamental equality of all people, but you ignore injustice when it benefits you.

In that case, does it really matter what your "core values" are? Or, perhaps, would you be better off simply deriving them from what you do, even if that's not always flattering? In which case, "procrastination" would head the list of my core values.

Which means I guess I'll have to think about it and work on self-improvement later.

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