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 2 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 4 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.

August 3, 2022 at 12:01am

#1036041

Books, Some

I don't have a lot to say about today's article. But I figured, if you're reading this blog, you might have a passing interest in science. And you know how to read. So...

Just five excellent science books you should read
Put these on your nightstand.

Nightstand? Didn't science figure out that to get good sleep, one should use one's bedroom only for sleeping and sex? I don't think science books qualify as the latter, though they might help with the former.

Fans of nonfiction enjoy diving into the infinite, intricate worlds that exist on our planet and beyond.

I quibble with "infinite," but since our lives are time-limited, I'll accept "more than we can ever explore."

Below, five science book recommendations for smart people with a range of interests.

And maybe also for dumb people who don't want to be dumb.

I Contain Multitudes, Ed Yong

Ed Yong makes it easy to understand the complexities of our bodies, perhaps muddling your definition of self in the process.

I haven't read this one, but we've discussed the human microbiome in here before.

Pale Blue Dot, Carl Sagan

It annoys me that the pictured book cover reads, "Author of Contact." Like that's what we should know Sagan from. Anyway, of course I've read this. Everyone has, or at least lies about it.

Where Buddhism Meets Neuroscience, the Dalai Lama

One of these things is not like the others...

To be fair, the elevator pitch: "Experts in the fields of consciousness, dreams, memory, psychiatric illness, meditation and more summarize the latest research and then engage in a dialogue with the Dalai Lama."

Still, I've about had it with books that claim consciousness is quantum and we can affect the world with our minds, or whatever. Maybe it is, but we can't, except the old-fashioned way through the medium of our bodies.

She Has Her Mother's Laugh: The Powers, Perversions, and Potential of Heredity, Carl Zimmer

This lengthy, meaty read provides a new framework for thinking about what we inherit from our parents and ancestors, DNA, genes, race, inheritance, and the moral and ethical questions surrounding new procreation technologies.

Might be worth a read.

Moonwalking with Einstein: The Art and Science of Remembering Everything, Joshua Foer

Join writer and co-founder of Atlas Obscura Joshua Foer on his thoroughly entertaining yearlong quest to improve his memory under the tutelage of top “mental athletes,” and discover the bizarre, niche world of the United States Memory Championships.

Aw hell no. We invented the internet, and computer files, and paper, and writing utensils, for a reason: so we didn't have to remember every damn detail. Considering what most of our lives are like, it can be a good thing to forget.

Incidentally, I've linked to Atlas Obscura in here before, and almost certainly will again. It's one of my favorite websites. Also incidentally, Foer's brother is also a writer; I've never read his stuff, but one of his semi-autobiographical fiction stories was adapted into a movie. It's called Everything is Illuminated, and it's absolutely wonderful. And topical right now, as it deals with Ukraine's troubled history.

So that's it. Like I said, not much commentary here. I've only read one of these books so far, but I might give some of the others a shot; it's been a while since I've gone on a nonfiction binge. I'm also happy to hear your recommendations.

3 Like • Comment • View 2 comments

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