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 7 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

about 12 hours 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

about 14 hours 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 ✍️

a day ago
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

a day ago
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

🐕GeminiGem🎁

Dec 23, 2024 at 12:56pm
In response to "Trash Pandas"

I wrote one of my Danger Dog stories based on a childhood camping trip that involved a raccoon stealing grapes from our cooler "Danger Dog's Camping Capers"

I had always heard that cockroaches will be the only thing that survives a nuclear war/apocolypse, but maybe it will actually be the raccoons.

4 Like

April 9, 2024 at 6:24pm

#1068297

Dark Side of the Moon

Made it back home. Amusingly, the weather did clouds and rain the entire 8-hour drive back—which, fortunately, didn't happen yesterday.

If you're hoping for a description of the eclipse, look elsewhere; it's been covered by better writers, and better photographers, than me, so I won't even bother. Just know that, whatever you've read, it's insufficient to describe the experience; and whatever pictures you've seen cannot do it justice.

I've seen some scoffs on the internet to the effect of "why bother with the hassle of traveling when you can watch it on video online?"

Leaving aside how sad their lives must be, or how it might feel to have one's sense of wonder surgically excised, I have to wonder if they ask that about everyone's experiences:

"Why go see a band in concert when you already have all their albums and can listen to them anytime?"

"Why bother going to a football game when you can watch it on TV?"

"What are you doing going to Disney World when you can watch internet videos of the lines and rides?"

"Why go camping when you can just look at pictures of trees and rocks?"

Now, granted, you won't catch me doing the last three, and my days of doing the first one are probably behind me, but I try not to yuck other peoples' yum.

Maybe some of them are just trolling. Maybe some honestly don't see the point in viewing celestial phenomena, and would rather go to concerts, sports games, amusement parks, or the (shudder) outdoors. Maybe an eclipse is "nerd stuff," but the fact is, everyone's a nerd about something. If it's not astronomy, maybe it's music, sports, theme parks, or hiking. Or beer or wine. If you really like something and seek its experiences and knowledge, you're a nerd about it.

As for me, I ended up seeing it from the grounds of a winery in Indiana, which may sound odd, but I'd been to that particular one before, and I knew they had good product. My friend and I got lucky that, when we got there, they still had viewing spots available, and we even got bling bags out of the deal. And they played Pink Floyd as the eclipse progressed, so everything came up Waltz. No, I didn't have detailed plans beforehand; I didn't see the point when, had it been cloudy, all that planning would have been mostly wasted.

Sick of hearing about the eclipse? Don't worry; that was very likely my last one, so no more from me on the subject... probably. Tomorrow, back to my regularly (and randomly) scheduled nerdery.

6 Like • Comment • View 5 comments

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