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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10 Most Recent Blog Comments:

Turkey DrumStik

about 7 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').

1 Like

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

November 27, 2018 at 12:32am

#946378

Have Your Kale and Eat It Too

I'm not on good terms with food.

I have almost no self-control, so left to my own devices, I'd be eating pizza and cheeseburgers every day.

It wasn't always that way. In a complete reversal of the way I've always heard things are supposed to be, I had more self-control when I was younger. I think I ran out, or maybe I just realized that having discipline never got me anywhere, while indulging myself got me immediate gratification. I figured I could force myself to eat kale, quinoa, and strawberries, hate life, and maybe get hit by a truck; or eat foods I actually enjoy like pepperoni pizza, and still maybe get hit by a truck after at least enjoying my meals.

Incidentally, I actually kinda like kale, quinoa, and strawberries - they're actually not bad mixed together, with maybe a bit of balsamic vinegar or lemon juice and olive oil - but if I had to eat that every day, I'd go looking for the truck.

It occurred to me that if I eat more healthy food, I might actually be fast enough to get out of the way of an oncoming truck, so I make the attempt. But I have to make it as automatic as I can, and ensure there's variety with, yes, the occasional indulgence that would give my cardiologist a heart attack, such as bacon or a grilled cheese sandwich. Or a grilled cheese sandwich with bacon. Dammit, now I'm hungry.

The key, I decided, was to take advantage of my innate laziness, and not get too complex with the food preparation. The less work I have to do, the less likely I am to say "Fuck it; I'm ordering pizza delivery." So I found a website that generates random meals based on calorie count targets, and it strives to balance macronutrients (carbs, protein, lipids) while providing a variety of fruits and vegetables.

The downside? It's not cheap, especially since I can't be arsed to drag my lazy self to the grocery store twice a week (if I only go once a week, everything spoils by day 7). Thus, I get delivery, as I mentioned a few entries ago. And there's a lot of wasted food. I haven't figured out how to use everything I buy before it spoils, since the food industry is hell-bent on making things difficult for singles unless they want to buy single-serving microwave meals. Like, say, one meal calls for celery and almond butter. The almond butter will last a long time, but I might use one stalk of celery out of the entire bunch, and the rest gets thrown away or fed to my housemate's guinea pigs. So my choice is: eat high-sodium prepackaged foods, no waste, and die of another heart attack; or buy fresh foods and be unable to use them all before they go bad.

Which reminds me of a story. One time when I was in a non-shit-giving phase, I went to the grocery store and loaded up on microwave meals, frozen pizzas, snack foods, beer, breakfast cereal, and other easy food. Went through the line and the cute cashier looked at my selection and asked, "So, you're single, huh?"

I chuckled. "How could you tell?"

"Because you're ugly."

Anyway, I could probably find a way to use the foods a little more efficiently, but that would take work to get the meal plans just right, and I'm allergic to work. It cuts into my game-playing time. Consequently, I usually just go with the random food it generates, and only change out meals if they involve food I can't stand.

So that's how I discovered that kale, quinoa, and strawberries makes for a pretty good salad. But I'd still rather have pizza.

8 Like • Comment • View 10 comments

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