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

December 17, 2020 at 12:02am

#1000350

Self-Restraint

"30-Day Blogging Challenge ON HIATUS" [13+]:
17. Maple Syrup Day
Did you know that this sweet and unique flavor originated in America?
Native American Indians were the first to harvest and boil the sap of the maple tree into a thick syrup.
Talk about, well, maple syrup, of course.

"JAFBG" [XGC]:
You have a new power this holiday season! You get to put one idea in everyone's head simultaneously and all of them will agree with it as fact. What idea are you pushing?

The one idea I'd put in everyone's head simultaneously is that I'm infallible and everyone should always agree with everything I say as fact.

Cheating? Sure. It's like wishing for infinity more wishes. Makes a shitty story, but a good life.

Of course, then I'd have to be really, really careful not to abuse said power, say by banning all holiday music from public places, or telling everyone that Bud Light isn't actually beer (which, to be fair, it isn't), or banning vertical video under penalty of death, or by convincing everyone that fake maple syrup just isn't worth it.

Because while fake maple syrup objectively isn't worth it, it's a hell of a lot cheaper, and some people just can't afford the real thing, and I'd hate for me to be the cause of anyone going broke because they bought liquid gold.

I was at some friends' house one time. They had a pre-teen kid, and we were all sitting around the table eating pancakes that his mom made. The pancakes were delicious, but the "syrup" was the fake stuff. Naturally, I didn't say anything, because I'm the guest, and I really try not to be rude.

So the kid took the "syrup" bottle and squirted half of it onto his pancakes, like pouring milk over cereal. Had it been the real stuff, the parents would have had to take out a second mortgage to afford it. Then I took the bottle and just put a little circle of "syrup" on mine.

The mom turned to the kid and said, "See how Waltz uses just a little bit of syrup?"

The dad turned to me and said, "I'll bet that's the first time you were ever used as a model for self-restraint."

I laughed, because it's true.

8 Like • Comment • View 9 comments

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