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:

Kåre เลียม Enga

about 5 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

about 23 hours 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

a day ago
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

tj-Merry Mischief Maker

Dec 23, 2024 at 4:55pm
In response to "Trash Pandas"

Being an avid camper, keeping items out of the reach of raccoons can be challenging. We've had them figure out how to open coolers, open chests, and even gnaw through rope used to suspend a cooler out of their reach.

2 Like

March 13, 2024 at 10:52am

#1066209

It's "Desert" Not "Dessert"

I pronounce it "collection of endorrheic basins," but apparently, that's wrong.

Why Do Nevadans Pronounce Their State’s Name So Strangely?
How you say it certainly says something about who you are.

Look, it's an occupational hazard when you make a career out of hydrology to see the world in terms of drainage areas.

Seriously, though, I, too, pronounced Nevada in the non-Nevadan way until I spent some time as a guest of someone who lives there. Then, I learned the One True Pronunciation, ensuring that never again would I be caught by that particular shibboleth.

How exactly is the name of this state pronounced? Nevadans say “neh-VAD-uh.” Non-Nevadans typically say “neh-VAH-duh.”

To get it out of the way, there isn’t really a “correct” or “incorrect” way to pronounce Nevada in any objective sense; both “neh-VAD-uh” and “neh-VAH-duh” are perfectly understandable to all English speakers, which is really the only thing that matters.

Yeah, not really. Watch what happens if you mispronounce quinoa, for example.

It is not unusual for the residents of a state to have their own pronunciation of their state’s name; regional accents and dialects can affect all kinds of words.

Which, I suppose, is how we get Mississippi when the people who live in that state call it Misipi. And don't get me started on Ar-Kansas.

Even worse, few countries pronounce their names the same way that foreigners do. I'm sure that the way we say "France" here in the US grates on the very last nerve of the French.

Proponents of “neh-VAH-duh” will often say, look, nevada is a Spanish word (meaning “snowy” or “snow-capped,” and the state’s name is probably derived from the Sierra Nevada mountain range, part of which lies within its borders.

And the area, like most of California, was once claimed by Spain and Mexico, which ex-Spains all the Spanish names in the area. Want to piss off some Southern Californians? Pronounce La Jolla like you're English, not Spanish.

The problem is that Spanish, being a much more sensible language than English, has five vowels, and five vowels only. (Well, if we’re not counting dipthongs. Or tripthongs. All languages are complicated but stay with me here.)

I think there are more problems here than that.

There are a couple of possible explanations for this phenomenon. One is that Nevada, being a fairly new and historically largely unpopulated state, traditionally did not have much to differentiate it. If you’re proud to be a Nevadan, what could you do to present that to the rest of the world? Until the creation of the Vegas Golden Knights NHL hockey team in 2017, the state had no major professional sports team, which is often a way to signify geographical pride.

You know who else doesn't have a major professional sports team? Virginia. And I don't hear too much crap about pronouncing my state wrong, except for the hillbillies out west who insist on Virginny.

In any case, the article (from AO) is like candy to me because it involves history, linguistics, sociology, and philosophy. So there's no hard science; nothing's perfect. In other words, everyone can learn something there, if only the "correct" pronunciation of Nevada.

8 Like • Comment • View 3 comments

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