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 8 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 10 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.

June 16, 2021 at 12:06am

#1011947

Singing Neutrinos

Nothing profound or, hopefully, controversial today; mostly just a lesson in how not to write a headline.

And maybe some physics... but no math, so don't run away just yet.

The singing neutrino Nobel laureate who nearly bombed Nevada
From desert to gold mine — Frederick Reines was a larger-than-life physicist who did larger-than-life experiments.

I mean, neutrinos sing? I admit I'm not up on all the latest advances in physics, but I didn't know we taught them to- oh. It's the scientist who sang.

Article is a book review, but also functions as a summary of the guy's bio. I shouldn't have to mention once again that I don't automatically shy away from book-shilling articles here on a writing site, but I just did anyway.

In the early 1950s, the physicist Frederick Reines and his colleague Clyde Cowan designed an experiment to detect neutrinos

From what I've read about physics, this was a Big Deal. Theoretical physicists can come up with all sorts of hypotheses, but it takes experimental physicists to support (or disprove) them. Very few physicists delve into both.

The experiment was to take place in the Nevada desert. A flux of neutrinos would be created by detonating a 20-kiloton nuclear bomb

I can see the grant proposal now. "First, we build an atom bomb..."

At the last minute, Reines and Cowan transferred the experiment to a nuclear reactor

Aw.

It's implied that the bomb went boom anyway, as they were wont to do back in the 1950s. However, I seriously doubt that "at the last minute" should be taken literally.

The neutrino-research community has mushroomed over the decades

It's always amusing to see a pun, intended or not, in articles like this one.

The article then goes into the aforementioned summary of Reines' life.

Neutrinos were nicknamed ghost particles because of their uncanny properties.

Turns out they're even weirder than scientists first thought, but that's another topic. Still, I wouldn't be surprised if, as with the "God Particle" (the Higgs boson) decades later, the media didn't latch on to this and create the entirely wrong impression.

But with no charge and a vanishingly small mass, they can be detected only indirectly, when they interact with another particle.

Okay, but technically, that's the only way to detect anything.

As Cole describes, Reines and Cowan began what they named Project Poltergeist at a plutonium-producing reactor in Hanford, Washington.

Project Poltergeist, plutonium-producing... come on, there have to have been more opportunities for alliteration in there.

Reines left Los Alamos in 1959 for the Case Institute in Cleveland, Ohio. Seven years later, he moved to the University of California, Irvine.

Note how there is nothing reported for Reines during his time in Cleveland. I like to think that this is because nothing good ever happens in Cleveland.

Anyway, like I said, nothing of tremendous import to most people, and this is more of an example of science book review writing than anything else. But there were enough little amusing things to make me want to include it here.

3 Like • Comment • View 3 comments

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