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🎶

about 21 hours 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.

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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

July 27, 2024 at 8:33am

#1074446

Still Planning

Time for a travel plan update, though it's probably going to be short. But maybe I have some other things to write about.

The travel agent I'm going with has a subcontractor for local knowledge. In this case, a French woman. And I'm completely on board with that, but the sub didn't get back to her before Wednesday of this week. And that matters because the agent took off for vacation on Wednesday, so that means no further information until, at least, Thursday of next week. Probably later, because she's the owner of the agency, so she'll be coming back to utter chaos that she'll have to deal with first.

Or, you know, maybe she's a better business owner than I was, and everything will run smoothly in her absence.

Must be nice to go on vacation when you're a travel agent. You can get yourself the best deals.

And there's not much else I can do until I at least know when I'll be leaving, which I don't yet. I tried searching for fun things to do in France, but Google keeps pointing me at the Olympics, and I don't give a shit about that.

Which, it occurred to me, may be hypocritical of me, as I've harped in here again and again about how there's no such thing as useless knowledge or experiences. And I do believe that. My rationale (or at least rationalization to make me feel better about myself) is that I also tend to avoid anything that's too popular. Like Taylor Swift (who I acknowledge has talent) or "reality" shows.

But yeah, I do have an aversion to sports. You know how kids sit bored in math class wondering how they're ever going to use this? You ever notice no one says that about gym class, even though the vast majority of the kids aren't going to go on to be professional athletes? "But, Coach, when will I ever use sit-ups in my career as a veterinary technician?" "Well, um, strong abs will help you lift big dogs onto examining tables."

My argument is that you never know when the stuff they teach you in school will be useful or necessary. Was it "necessary" for me to spend high school in orchestra and drama class, let alone Latin? No, probably not. And I didn't know I was going into engineering until like senior year, so even math was questionable. But I learned all that shit anyway (and promptly forgot most of it).

The point being that just as strong abs are generally a good thing (something even I can acknowledge) even if you're not a pro athlete, so it is with a strong mind.

Now if only schools would emphasize that sort of thing instead of being all about the football team, we might actually get somewhere.

What does this have to do with travel? Well, nothing, except that maybe I can stretch (another good exercise) and claim that travel broadens one's perspective, so it's the same sort of thing. But, mostly, I'm rambling because I didn't accomplish anything else in terms of travel planning this week.

Next week, I'm going to look into relatively cheap laptops so I can bring one on the trip. Like a Chromebook or something, so I don't have to use my phone to make blog entries. I don't want to take my expensive gaming laptop with me (the one I'm typing on now), so this seems like a reasonable thing to do. Besides, it never hurts to have a backup here at home in case this thing blows a circuit one day.

And then I have to see about getting internet there. I'm well aware that they're ahead of the US in that regard, but that doesn't mean the systems are compatible, kind of like how I have a plug adapter to handle the different electrical outlet configurations.

5 Like • Comment • View 4 comments

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