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.

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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.

October 29, 2019 at 12:24am

#968586

Fantastic

https://www.thrillist.com/entertainment/nation/best-fantasy-book-series-sci-fi-s...

The 21 Best Science Fiction and Fantasy Book Series Ever

"Best" is usually subjective. They're still wrong about some of these.

We’ve done the hard work for you and rounded up the 21 best science fiction fantasy series of all time, in no particular order.

I'll give 'em credit for not putting it in a countdown-style slideshow to generate more clicks. As a reward, I'm sharing this and maybe they'll get a couple more clicks.

For the sake of tidiness (and our own sanity), we’ve limited this list to series that include at least three books, and that are either completely finished or have no further books currently planned (so, no A Song of Fire and Ice)

That's good, because I got bored with that bloated tripe about halfway through the fourth book. Okay, I'm being unfair - Martin is a good writer, but when I drop a book halfway through, it's for good reason: I just quit caring what's going to happen.

Couldn't watch the series, either.

Now. Some of the series in that list, I've read; some, I haven't. Unlike some people, I don't have an opinion on the ones I haven't read.

The Vorkosigan Saga (1986-ongoing) by Lois McMaster Bujold

I like this series a lot, but I really hate Bujold because she got her first novel published on, from what I've heard, the first try. Bitch.

The Wheel of Time (1990-2013 by Robert Jordan (with Brandon Sanderson)

This series ain't all that. Remember how I said if I quit a book halfway through, it's because I just don't care? Well, I got about 1989 pages into the 2000-page first book of this series, right when things are supposed to be all climax-y, when the book's plot is being wrapped up and the stage set for the next 89 books, and threw the thing at the wall.

When Jordan died and I heard Sanderson was going to wrap things up for him, I thought about going back and trying again - I like Sanderson's writing a great deal, and I figured if he cared enough to do the work I should at least see what all the fuss was about, but... you know... squirrel!

The Lord of the Rings (1954-1955) by J.R.R. Tolkien

Come on, do we really have to include this one?

His Dark Materials (1995-2000) by Philip Pullman

Let me not mince words, here: this series is indefensible. About the only good thing about it is: bears in armor. I mean, that's epic. But everything else about the series actually sucks. Unlike some of the other books I mentioned, though, I actually finished it. That's 24 hours of my life I'm never getting back.

The Hitchhiker’s Guide to the Galaxy Series (1979-2009) by Douglas Adams

Two of my favorite things are science fiction and comedy. When someone combines the two and does it well, it can be amazing. Also, these books are so ingrained in pop culture that you're lost if you don't read them - kind of like Star Wars.

Mistborn (2006-2008) by Brandon Sanderson

I'd pick The Stormlight Archives over Mistborn when it comes to Sanderson, but apparently the list is about completed series (even though the status of the Vorkosigan saga might make the Bujold entry an exception). Still, Mistborn is a fine series by an excellent author who is amazing at crafting epic fantasy.

There are also three fantasy series that are conspicuously absent from this list:

Amber by Roger Zelazny

Zelazny, like Jordan, was taken from us too soon. Unlike Jordan, he pretty much finished the Amber novels - though I think he wanted to write another set in the series. There are ten books in all, and the first book, Nine Princes in Amber, served as my personal introduction to fantasy.

The Vlad Taltos novels by Steven Brust

I've read this series so many times it's pathetic. The first book, Jhereg, contains what I consider to be the greatest opening line in all of fantasy (at least all that I've read). Again, though, the series might not be actually concluded.

Chronicles of Alera by Jim Butcher

Butcher is better known for the Dresden Files, a modern fantasy series. But it's definitely still in progress. Alera is a five-book (if I recall correctly) high fantasy series that's just a great read.

Anyway, that's my opinion, which of course you can take as truth.

I'm kind of surprised Harry Potter didn't make the list. Like Pullman's crappy series, it's targeted at a younger readership, which is fine. The first book was kind of painful to read, but the author got better as she went along. And like Hitchhiker's, it's part of pop culture now and there's no going back from that.

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