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:

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').

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

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

1 Like

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

December 27, 2020 at 12:01am

#1000882

Nuttier than a...

"30-Day Blogging Challenge ON HIATUS" [13+]:
27. National Fruitcake Day
Write about your opinion of Fruitcake.
If you don't like them, you haven't had mine.

Counterargument: if I like it, it isn't actually fruitcake.

I don't know who first said it and I can't be arsed to look it up, but there's this idea that each family has only one fruitcake. Whoever gets it at Christmas shoves it in their freezer and regifts it to a different family member next Christmas, and they put it in their freezer, and the cycle continues until the heat death of the universe.

Now, I don't come from a fruitcake family, but I've had occasion to try other peoples' fruitcakes from time to time, and I just have one question:

Why? For the love of all that is right and pure in the world, WHY??!

Each of the various components of fruitcake is, usually anyway, just fine on its own. Put it together and you end up with the culinary equivalent of plaid and stripes, or socks with sandals.

I will grant that the person who wrote this prompt (it was Lilli 🧿 ☕) probably makes some delicious cake. She might even call it "fruitcake." But this is like owning a Mercedes and calling it a Chevy.

I've heard the "If you think you don't like x, it's only because you haven't had mine" argument before and, all due respect, it is bullshit.

Take eggplant, for example. That's aubergine for my Brit friends. A typical conversation for me might go like this:

"I don't like eggplant."

"Oh, that's only because you haven't had mine."

*I try the eggplant dish*

"...I hate eggplant."

At some point, as I refuse to fake an allergy just to get me out of eating something, I started saying instead: "Eggplant is not actually food." This usually works. When it doesn't, I end up subjected to either a) a dish that is, objectively, made very well, but since it contains eggplant, I can't stand it; or b) a dish that so thoroughly covers up the disgusting taste and/or horrid texture of eggplant that one wonders why the dish isn't simply made without the offending material.

It is, on the other hand, absolutely true that there are some things that, if not cooked properly, just don't taste very good; but if made with skill and knowledge, can be delicious. Zucchini (that's courgette for my Brit friends) is one such foodstuff. I always thought I hated zucchini when I was a kid, but the truth was I hated the way my mother cooked the stuff.

Hell, the way my mom cooked, I was convinced that I didn't like chicken.

Still, there would be one way for me to change my mind about eggplant, or fruitcake for that matter: tell me I can't eat it. "I'm sorry, Mr. Waltz, but you have a rare illness. You'll be fine as long as you never eat fruitcake. But if you do, you'll end up in the emergency room or possibly die."

In such a scenario, all I'd be able to think of is how delicious fruitcake would be right about now.

That may sound farfetched, but that perfectly describes me with grapefruit when I started taking statins. Never cared for the stuff until the doctor told me I could never eat it again, at which point it was all I craved. This ebbed over time, but for a while there, grapefruit (I have no idea what Brits call it) might as well have been chocolate for all the cravings I got for it.

Still, there's little chance of that happening with fruitcake, so I think I'm safe on that front.

7 Like • Comment • View 6 comments

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