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!

a day 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

a day 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.

May 1, 2019 at 12:23am

#957959

Mayday

Hooray, hooray, the first of May!
Outdoor fucking begins today!

It's a new month, so it's a good time for me to get back to daily blogging. Maybe. (Pun intended, as always.) I'm participating once again in "30-Day Blogging Challenge ON HIATUS"

[13+]

Crazy as it may sound, we are now officially 1/3 of the way through 2019. Write about some of your goals and plans for the remainder of the year. What are you looking forward to?

I'm wary of making goals. Or plans. When I inevitably don't fulfill them, I get even more wary next time.

I'll tell you what I'm looking forward to, though: warm weather. I'm pretty sure we'll get some of that. While my area was spared the recent unpleasantness that happened in some of the middle states, I got tired of the cold weather damn quickly.

In previous entries, I've outlined my dislike of the cold. "So, Waltz, why not just move?" Well, true, I could, but apart from a few months out of the year, I rather like it here in Virginia. I've been all over the country (except for Nebraska, Alaska and Michigan, none of which are in the top 40 candidates for states to move to anyway), and while I enjoy certain places, I'm happy to merely visit. Too much traffic most places, except for where there's nothing around, in which case there's nothing around. Here, there are nearby purveyors of fine alcoholic beverages, and I don't have to sit in traffic (or, more precisely, sit in a rideshare vehicle which is sitting in traffic) to get to them.

But that's not the question, is it? To misquote an entirely too popular catchphrase, summer is coming. And, for the most part, I intend to sit here on my deck and enjoy the utter lack of snow. Assuming, of course, we don't get a volcano, nuclear war, or meteor strike that blots out the sun.

Patient and sharp readers will have noticed an inconsistency here. I rant about cold weather, and then I rant about the accursed daystar. Well, I'm not required to be consistent. Self-contradiction only makes me more interesting, right? "I am large; I contain multitudes."

This is easily resolved, though: I only go outside to sit on the deck, which has a patio umbrella. I am within two feet of the door to my house at all times, and if the blasted fusion sphere starts to annoy me, I can go inside where it's properly air-conditioned.

Still, getting back to plans, I'm hoping to do a bit more traveling this year. Maybe go to Vegas in August or September. Almost certainly visit California in December, if it's still there. Apart from that? Stay warm for as long as I can, until the cycle turns again.

And write. Against all odds and expectations, I've been steadily participating in "I Write in 2019"

[E]. Just 8 more months of that to go...

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