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

November 11, 2020 at 12:02am

#998107

Fast Food

Wait... you can make meals?

PROMPT November 11th

What is your favorite meal to make when you are really hungry?

Delivery pizza.

No, I'm not joking.

For the last couple of years, I've been on a meal plan. During the first year, that plus exercise caused me to lose a lot of weight, which is a good thing. Then the pandemic came along, and I started drinking more and canceled my gym membership (yes, it's possible to do that), so the meal plan, at best, now helps me keep off what I've lost. It also has me eating smaller meals more often, which usually keeps me from getting too painfully hungry.

Also, I've been single for a while, so I don't cook much anymore, apart from a few things in the meal plan. It's not that I never learned how; I used to be a passable cook. it's just that I can't be arsed. You know me: maximum return for minimum effort. If it's just for me, I don't bother with anything fancy or complicated; I don't need to show off for myself.

Like anybody, though, I'm not perfect. In fact, I'm less perfect than most. So I don't always stick to the plan -- hence, the occasional pizza. I will say that's a lot more rare now than it was before I began to lose weight. It's almost as if there was a correlation there. I've also all but eliminated other kinds of fast food from my intake.

Things are starting to get colder now, though, and I might have to break down and cook a pot of my chili. But the chili wouldn't count for the prompt; it takes way too long to prepare and cook when I'm actually hungry.

When it comes to "making" food while starving to death, it needs to be something quick and easy, like a sandwich -- but I usually don't have sammich stuff lying around because it goes bad before I can eat it. What I should probably do is cook the chili and freeze serving sizes of it, so when the mood takes me I can just thaw some and plop it into a bowl. But it's not like me to plan ahead like that.

In case you're wondering (you're probably not, though), there's a pizza place near me that is not crappy chain pizza (e.g., Domino's or Papa John's) that usually delivers in 20-30 minutes, unless there's something like a sportsball game going on so that they're busy and there's traffic. So the time between "I'm really damn hungry" and "nom nom nom" is pretty short. The place has been in business as long as I've been in town; it was the first phone number in Charlottesville that I memorized, though these days it's easier to order online. As far as I can tell, their recipe hasn't changed in 40 years.

There's another restaurant near me that has better pizza, but sadly, they don't deliver. They do takeout, however. I haven't been there in a while. Of course, now that I've thought about them, I'm going to have to go. So thanks for ruining my diet.

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