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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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 3 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 5 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.

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.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

April 8, 2021 at 12:03am

#1008003

Not-Reading List

As yesterday was National Beer Day, I can't even right now. But I'm going to try anyway. I've encountered this writer before, with very mixed results.

7 Fiction Books That Change The Way You Think

Over the past three years, I’ve read more than 200 non-fiction books.

Must be nice to have that kind of time. I'm retired and I don't have that kind of time.

I’ve dived into Philosophy, Marketing, Productivity, Evolution, History, Biographies, and many other books you read to learn something.

No wonder I've encountered him before; a lot of those are my thing too.

One thing I’ve noticed is that non-fiction books of the past ten years are not boring to read.

Gotta agree with that point. People shy away from non-fiction on principle, I think, the way I avoid jazz and opera.

Then he segués into the actual topic of the post, non-non-fiction, aka fiction.

I’ve made a list of 7 fiction books that have inspired me. You won’t find the cliché books on this list. We all know The Catcher In The Rye, Lord Of The Flies (I really hate that book, it’s so obvious), To Kill A Mocking Bird, and so forth.

Also gotta agree on Lord of the Flies. Thinly-veiled anti-humanist propaganda. Okay, not even veiled.

1. Where’d You Go, Bernadette by Maria Semple
This book was recommended to me by a reader. It’s not something I would stumble upon myself.

Too good for it?

Where’d You Go, Bernadette is an entertaining and creative novel about weirdoes in Seattle.

Nope. Next?

2. Naïve. Super by Erlend Loe
Another funny and entertaining book. Loe is from Norway, and I like his minimal style. It’s a story about a young kid who’s searching for meaning in life.

While minimalist styles appeal to me, I'm still thinking "Oh, another kid searching for the meaning of life, probably born from the author's inner child navel-gazing." Next?

3. Crime and Punishment by Fyodor Dostoyevsky
Let’s get a little serious. This book is an examination of human suffering. If this book doesn’t change the way you think about people, nothing will.

I've actually never tackled this one, but always thought I should -- until I read this article. I'm starting to think that maybe this author is more of a negative example. As in, if he likes it, I won't.

4. Fight Club by Chuck Palahniuk
The only very familiar book on this list. I’ve referred to this book more often and I still enjoy it after all these years.

Okay, look, that book was made into one of my all-time favorite movies. Not because of the surface elements that people tend to focus on, but more about the subtext. I never read the book. But I made the mistake, once, of trying to read a different book by Palahniuk, and... I'll just stick to the movie, thanks.

5. Ask The Dust by John Fante
My favorite writer, Charles Bukowski, was influenced by Fante. In Ask The Dust, you read the story of Arturo Bandini, a struggling writer in 1930s Los Angeles.

"Write what you know" is questionable advice in the first place (I prefer "know what you write"), and writers writing about writing writers is the worst kind of cliché. I'm going to go out on a limb here and predict that the story involves a torrid affair, probably with a much younger woman. I could be wrong, but I'm just not feeling it. (I'll read the hell out of Bukowski, though.)

6. Death With Interruptions by Jose Saramago
We all die, right? But what if that wasn’t the case? A lot of people are afraid of death, but in this novel, people don’t have to be afraid anymore. Because on the first day of the new year, no one dies.

Yawn.

7. Cathedral by Raymond Carver
Because Raymond Carver wrote short stories, he’s never included in any ‘top novels’ lists. And that’s a shame.

No opinion, but given the rest of this list, pass.

Again, I could be way off about these things. Maybe they're worth reading. Maybe not. This article doesn't sell me on the former, though. If I were to tackle any of them, though, it'd be Dostoyevsky, because Russians have a wonderful optimistic attitude toward life and love happy endings.

That's sarcasm. Except for the part about wanting to read it.

Anyone here ever read any of these? I think I'll need a second opinion. Otherwise I'm inclined to read literally any other book than the ones listed here.

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