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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Write_Mikey_Write!

about 6 hours ago
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

about 8 hours ago
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.

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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.

December 5, 2023 at 8:14am

#1060561

Cracked

No journey is without its pitfalls, or, in my case, rockfalls. I don't even know when it happened, but somewhere in Wyoming or Utah, something smacked my windshield, cracking it.

Not a big deal, usually. These things happen, and it's one reason to have insurance and such. Certainly better than the last time something smacked into me on a road trip. The crack's not even on the driver's side, so not really interfering with my view or anything.

But the crack keeps spreading. Slowly. Relentlessly. Like the doom you know is following you everywhere you go; you try to ignore it but every time you glance over, there it is, looming. Looming doom. Gloom.

So when I got to Reno, the crack (it's actually a double crack looking a bit like the Tigris and Euphrates) creeping across at its less-than-a-snail's pace, I stopped at the Subaru dealer/service. This, incidentally, is one great benefit of modern technology: On the way in, I simply asked my friendly navigator, Google, to find it for me and direct me there. Let's see a paper map do that, Luddites.

Now, to be clear, this is not something I'd worry about too much back home. Make a service appointment, get it taken care of. I don't think it even takes all that long to do. But the thought of driving back across the country with the growing crack didn't fill me with much confidence.

Unfortunately, they can't get to it until next week, at the earliest. Not because of a wait time, but because they have to get the glass in. I wasn't planning on being in Reno next week. I was hoping to be in Vegas, with my visit to California over the weekend.

But, unexpected change is part of the adventure of travel. The only thing that pisses me off is the cost. It's just enough more than my insurance deductible that it might be worth filing a claim for the difference, but then I don't know if insurance will use it as an excuse to raise my rates, negating the benefit of using it.

And if they can't get to it next week, I'm screwed.

Either way, it's a gamble but, behold, that is what I'm in Reno for.

8 Like • Comment • View 4 comments

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