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').

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

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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 25, 2020 at 12:01am

#1000802

Out of Your Gourd

"30-Day Blogging Challenge ON HIATUS" [13+]:
25. Pumpkin Pie Day
Are you a fan? Why or why not.

Life isn't binary.

I'm okay with pumpkin pie. Well, most pumpkin pie. The canned stuff isn't so great. And -- shh, don't tell anyone -- I actually like pumpkin pie spice. Not enough to ever crave it, though there is one pumpkin beer that comes out every fall that I just need to acquire at least once a year.

I did a Comedy newsletter about pumpkin spice way back in September: "Pumpkin Spice"

. Go ahead, read that editorial if you haven't already. This isn't the only place where I do comedy.

So imagine my surprise when I find out that today, December 25, is officially (by whatever means people decide such things are "official") Pumpkin Pie Day. As far as I'm concerned, that season is over. Now is the season for other spices, and for stouts and port wine.

Still, pumpkin, and pumpkin spice, could disappear tomorrow and I wouldn't miss it too much. I don't love it. I don't hate it. So when I say "I'm not a fan," I don't mean I'm an anti-fan; I simply mean I like it well enough and will eat it if it's around. Saying "I'm not a fan" apparently means something other than its plain denotation, for some people, so I feel like I have to make it clear where I stand: on a scale of 1 to 10, it's a solid 6.

You know what else today is?

Today is No "L" Day.

Personally, I think every day should be Punday. Find an excuse if there isn't an obvious one, like today. Tomorrow would be easy enough; plenty of pun material in Boxing Day. Next week could be New Beer's Eve, where the goal is to try a beer that's new to you (a thing that is getting harder for me all the time).

But that would also make this Pun-kin Pie Day, so maybe we need to celebrate Pun-kin Pie Day on some other occasion. Sometime in October, maybe, because come ON, all the pumpkins are gone by now but there are always puns to be made.

And hey, because it's No "L" Day, let's have a...

Merit Badge Mini-Contest!

Comment beow without using the etter between K and M in the aphabet, and say what your favorite hoiday food and/or beverage is. The one I ike best gets the person who posts it a Merit Badge tomorrow. The deadine is midnight today, December 25.

Unfortunatey, my favorite hoiday food is atkes...

7 Like • Comment • View 9 comments

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