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.

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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

February 26, 2023 at 9:21am

#1045558

Revisited: "Random Thoughts"

It's Throwback Sunday (maybe I should start doing these on a Thursday), and the random number generator gave me another one from 2009, mid-September: "Random Thoughts"

Sadly, this is mostly not my work. While I'm certainly not above quoting sections from an article I link to comment on, it isn't usually my style to just copy something whole-cloth, even if it is something that was circulating widely at the time. I don't know; I may have done it more in the distant past—I don't remember, which is one reason I do these retrospectives. But I don't do it much, if at all, these days. My blog is to emphasize my thoughts, not someone else's.

The entry does start out with me:

A friend of mine just discovered the wonders of email.

Again, this was 2009. I think I first got an email account in 1994, unless you count the one the university assigned to me as a student in the eighties.

This means that she's currently forwarding every bit of glurge and misinformation on to all of her hapless friends.

I'm at a loss to remember who this was. Probably she's all over Failbook and DikDok now.

I was just about to relegate her latest recirculated bit of "wisdom" to the compost pile when I accidentally looked at it.

And laughed.

What can I say? Wade through enough shit and eventually, you'll find a penny.

Re-reading these now, I don't think they're quite as funny. I won't paste all of them again here.

I wish Google Maps had an "Avoid Ghetto" routing option.

Probably racist, definitely classist.

I totally take back all those times I didn't want to nap when I was younger.

Inertia is a thing. If I'm awake, I want nothing more than to stay awake. If I'm asleep, I want nothing more than to stay asleep.

There is a great need for sarcasm font.

Comic Sans is the Official Sarcasm Font.

I would rather try to carry 10 plastic grocery bags in each hand than take 2 trips to bring my groceries in.

Wow, that one didn't age well.

Map Quest really needs to start their directions on #5. Pretty sure I know how to get out of my neighborhood.

Nor did that one.

Bad decisions make good stories

This one, however, is timeless.

Can we all just agree to ignore whatever comes after DVDs? I don't want to have to restart my collection.

Well, that didn't happen.

While watching the Olympics, I find myself cheering equally for China and USA . No, I am not of Chinese descent, but I am fairly certain that when Chinese athletes don't win, they are executed.

Eesh.

I hate when I just miss a call by the last ring (Hello? Hello? Darnit!), but when I immediately call back, it rings nine times and goes to voicemail. What'd you do after I didn't answer? Drop the phone and run away?

I have no idea what this means anymore.

As a driver I hate pedestrians, and as a pedestrian I hate drivers, but no matter what the mode of transportation, I always hate cyclists.

This hasn't stopped. It needs to. Desperately.

I think the freezer deserves a light as well.

I have a warped sense of time, but I'm pretty damn sure my current refrigerator is one I bought long before 2009. Its freezer features a lightbulb.

Well, that's enough of that. Some of the ones I didn't re-glurge-itate here are still legitimately funny, but these days, instead of being forwarded around in email, they'd all be pasted on top of an image of some sort. Because our attention spans really are SQUIRREL!

3 Like • Comment • View 3 comments

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