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:

tj-Merry Mischief Maker

about 21 hours ago
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

a day ago
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

🌖 HuntersMoon

Dec 23, 2024 at 10:04am
In response to "Trash Pandas"

Just wait until we team up with the cats...

4 Like

Jayngle Bells

Dec 23, 2024 at 10:03am
In response to "Trash Pandas"

The back of my property is sheltered by buildings and cedar trees, so I live on a "racoon highway." Tinfoil works until one takes it for the team and moves it. The only scent that somewhat deters then is ammonia - but they alter their path within the already preferred walkway, not avoid it completely. They generally leave the garbage bin alone, but that's because of the bears, not because of anything we do 😂

I've had more wildlife problems in the city than I ever did in the country. The first time I saw a deer up close? In the middle of my street directly in front of my house. Probably looking for the trash panda party. Lol

4 Like

Annette

Dec 21, 2024 at 11:59am
In response to "Neutral Zone"

It made me happy that I was able to like it. I take the small victories.

1 Like

tj-Merry Mischief Maker

Dec 20, 2024 at 6:06pm
In response to "To Err Is Human"

Right from the beginning I find myself asking, "How many times can anything go extinct?" On a side note, the other day while shopping I saw a neanderthal in the produce section. He was trying to fit in with modern clothes, but it was pretty obvious he was a neanderthal.

1 Like

Annette

Dec 20, 2024 at 1:00pm
In response to "To Err Is Human"

Comments work.

"Like" button sends me this message:

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Annette

Dec 20, 2024 at 12:58pm
In response to "To Err Is Human"

Can I leave this comment?

Wordsmitty ✍️

Dec 19, 2024 at 9:03pm
In response to "Five Seconds"

Way, way back when I was little, it was a three second rule that I remember. Sometime since it was upped to five seconds because of all the chemical preservatives that are pumped into everything now.

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August 25, 2024 at 9:46am

#1075694

Revisited: "Journeys"

Today's trip through the Wonka tunnel of time takes us back about five and a half years, to the end of February, 2019. Or about a month after my last Revisited entry. Random numbers will do that.

The entry itself, "Journeys"

, was mostly just a personal update, utterly uninspiring and uninspired. This happens sometimes, too.

Finally, the last day of the hated month of February.

I don't remember when I first noted to myself, "You know? I really, really hate February." But clearly, it was over five and a half years ago.

Unfortunately, the weather report here indicates more cold days ahead, and possibly s**w. But at least the end is in sight: three weeks to the equinox.

Not a big fan of winter in general.

If I can make it that far without straying too far from my healthy-eating-and-exercise plan, begun on the solstice, I'll consider it a win. Then it won't feel so bad when I inevitably fail.

See, this is why I'm a pessimist: I can smugly assert that I totally expected to fail, so I was right, and I love being right.

There follows a couple of links to WDC activities, one of which is currently inactive, the other of which is, as I understand it, on its final round.

I'm starting to get antsy for travel again, too. Part of that, though, is the crappy weather we've been having (normal for February in Virginia, but still crappy), so we'll see if I still have the urge in, say, April.

I don't remember, and can't be arsed to look up, if I actually went anywhere in 2019. That long ago, in the Before Time, stuff starts to blend together into some kind of idyllic swirl, an innocent's last gasp before everything went to shit a year later.

It's nearly the end of August now, and already I'm mourning the end of summer.

Oh well. Soon, Oktoberfest beers will be available, and those always make the transition to autumn more tolerable. And, of course, I have a journey to look forward to.

2 Like • Comment

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