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 6, 2019 at 12:10am

#962131

Master Peace

Make a list of five things you wish you could be a master of. Be sure to explain why you chose what you did.

I don't have such wishes anymore.

It's not that I don't want to master anything; it's that time has convinced me that the important part of being really good at something is the learning and practice part - the "getting there" bit, not the "being there" situation.

This is, of course, directly analogous to my travel philosophy: that there is no destination, only journey.

But, since I consider these prompts excuses to think of things I might not think of otherwise, I'll give this a shot. So here, in no particular order, are five things I wish I could be a master of.

1. Writing. That should be obvious, given what website we're perusing. Of all the items on this list (or so I say now, before I've finalized the other four), this is the only one I'm actively working on. As I've said before, I don't think it's possible to achieve perfection in this; there are just too many things to learn, practice, and coordinate. Also, "mastery" looks different for everyone. But there's one way to know when it has been achieved: when one is published, widely read, and possibly rewarded for one's work. I don't think I'll ever get there, but like I said - it's the journey that matters to me. Why? Because I think that words can change the world, and I still have an urge to leave my mark, somehow.

2. Myself. Yeah, I know this is a little off-key for this list, but it's what came to mind. As with, I believe, most people, I'm always torn between what I want and what I want, pulled in different directions, perhaps by the proverbial

and

on my shoulders - and I don't even believe in the supernatural. For instance, the other day, I went out to lunch with an old friend. On the menu was a pastrami reuben. Also on the menu was a steak salad. The reuben, obviously, had the higher calorie count, a potentially debilitating quantity of sodium, and an overdose of the kind of dietary lipids that are not conducive to heart health. As I am still working on weight loss - successfully, I might add - I wanted to order the salad, which featured loads of leafy vegetables, lean meat, and the option for dressing on the side for portion control. But I also wanted to order the reuben, because pastrami is delicious. Naturally, I ended up ordering the reuben, and I'm still beating myself up over it, even though it was, indeed, delicious. So I wish I could be a master of myself. Why? So I would not make self-destructive choices that are opposed to my longer-term goals.

3. Music. This one's pretty simple, really; I just always wished I had musical talent. Piano, violin, guitar, voice, whatever. Why? Because I can express things with music in a way that can't be done with words. I mean, I have enough technical ability to do so to some extent, but it would be nice to not have the neighbors calling the cops because they think I'm torturing my cats. (On the other hand, lack of talent in other areas is what pushed me into writing, so, as a blind person might find their other senses heightened, it's probably best that I don't split my efforts. Still, this list is, as I see it, more about wishes than reality.)

4. Language. Though, honestly, I haven't seriously tried to learn another language in a long time, I don't think I'd be very good at it. But I wish I could be. Why? So I could travel to other countries with greater confidence and communicate with people from other cultures.

5. Baiting. Why? Because I cannot resist a pun, even when it's obvious and painful to other people. Especially when it's obvious and painful to other people.

But, as I noted above, it's not about being a master, at least not for me. Dreams are shadows; goals are elusive; the destination is always over the horizon. But the journey is meaningful.

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