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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Show Recent Comments

10 Most Recent Blog Comments:

tj-Merry Mischief Maker

about 16 hours ago
In response to "Extro Special"

I'll also use the spelling extrovert because if I use extravert my spell checker flags it. In college psychology our professor termed his own words, innervert and outervert because he thought they fit better. I, however, thought they sounded like definitions of belly buttons.

1 Like

Kåre เลียม Enga

about 22 hours ago
In response to "Extro Special"

I probably fit omnivert best. I'm temperamental.

Words change... definitions change... we change.

1 Like

tj-Merry Mischief Maker

a day ago
In response to "Sensational"

They say carrots can improve your eye sight, but it's been proven that drinking alcoholic beverages can make you see double.

After stating this, I find myself wondering why hasn't anyone tried fermenting and distilling carrots and marketing it as a vision tonic?

2 Like

🌖 HuntersMoon

a day ago
In response to "Sensational"

OK, look around you and observe (where possible) the reality of the newly revealed "facts." It's pretty clear that "Smartphones make you a hell of a lot of folks stupid."

2 Like

Elisa: Snowman Stik

a day ago
In response to "Sensational"

Thank you for reminding me to check on Retraction Watch.

https://retractionwatch.com/

3 Like

tj-Merry Mischief Maker

Dec 26, 2024 at 4:20pm
In response to "Gray Matters"

I wonder how many nine year old people have gray hair? I also wonder how much stress most nine year olds have?

3 Like

Wordsmitty ✍️

Dec 26, 2024 at 1:07pm
In response to "Gray Matters"

"who were between age nine and 39," - so the old folks need the rejuvenation formula first to turn back the years.

I wonder if anyone has studied why hair goes gray in certain places and not everywhere. Maybe different kinds of stress?

3 Like

🌖 HuntersMoon

Dec 26, 2024 at 10:00am
In response to "Gray Matters"

I've always believed "better gray than gone away..."

2 Like

tj-Merry Mischief Maker

Dec 25, 2024 at 3:02pm
In response to "A Mammoth Discovery"

This makes think of a book, "Evolution and Genomic Diversity" by Gene Poole.

1 Like

tj-Merry Mischief Maker

Dec 24, 2024 at 5:16pm
In response to "Hot Shoulder"

Maybe if we say, "Betelgeuse" three times in a row we can witness it.

1 Like

February 8, 2024 at 11:05am

#1063762

Freeze Frame

I'm not going to have too many comments on the article I'm sharing today. It's more for informational purposes; these days, everyone is a photographer, and while phone cameras do a hell of a lot of the work for you (more than most people can appreciate), there are still things anyone can do to improve their picture-taking ability.

How to take better photos
Anyone can learn the principles that are essential to capturing quality images. Follow these tips and see the difference

Before the era of social networking sites, creating and sharing photographs was more deliberate and less instantaneous, which made picture-taking feel special. Families cherished the physical print – a link to the past with sentimental value – and kept their precious memories in albums, rarely showing them outside the family. Today, people commonly take photos not only to serve as memory cues but to tell others who they are, what they care about, and how they feel.

One might be tempted to think because I learned photography and even made a bit of money from it before digital cameras were a thing, that I'd have things to say about how kids these days have it too easy, that photography used to mean something, dammit, and that I'd yearn for the good old days of film and the techniques involved in developing it.

While I'm glad I got that experience, I'm also something of a technophile. Digital cameras can be amazing, and they've democratized the act of recording images for posterity.

In this Guide, I will provide some photographic principles and specific tips for casual, amateur and aspiring photographers on how to take better photos. By ‘better photos’, I mean appealing images that evoke emotions in the viewer and capture the essence of a subject or scene (and that resonate with how our brains make sense of the world).

I find that no matter how good you are, or think you are, at something, learning more about it, even some of the so-called basics, can help. Even us engineers were expected to keep learning throughout our careers.

So. Like I said. I have no real comments on the article; I think it's full of good information, whether you're using your smartphone as a casual snapshot-taking device, or have invested inspent money on a fancy DSLR (it's only an "investment" if you expect to make money from it).

Everyone's a photographer now, but that doesn't mean they're all good at it.

3 Like • Comment • View 1 comment

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