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 20 hours 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🎁

about 24 hours ago
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

a day ago
In response to "Trash Pandas"

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

4 Like

Jayngle Bells

a day ago
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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2 Like

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.

1 Like

tj-Merry Mischief Maker

Dec 19, 2024 at 3:43pm
In response to "Five Seconds"

I also ate carrots right out of the garden growing up, I also picked and ate fruits and berries growing in the wild without washing. I do remember food dropped on the floor was either rinsed off and then eaten, or if it was something not easily rinsed, like buttered toast buttered side down, we gave it to the dog.

In our house, there's not a five second rule; unless it's something dogs can't eat, it's whichever one gets it first.

2 Like

November 24, 2024 at 9:37am

#1080425

Revisited: "Plus Ça Change..."

My dip into the past this morning takes me all the way back to January of 2022, when I was cold and disease raged across the land. So, not much different from today: "Plus Ça Change..."

In it, I responded to a then-current prompt from "JAFBG"

[XGC], which is still active and other bloggers should totally check out the active prompts.

The prompt was: "Imagine the pandemic never happened. How do you think your life would be different now, if at all?"

Most of us have forgotten all about it, apparently.

...okay, look, I'd like to say that the only thing that would be different is that I wouldn't have canceled my gym membership. But let's be real: I still would have canceled my gym membership. Eventually. Because I'm lazy.

I still haven't re-enrolled. Laziness is my only excuse there. There was a long stretch, before everything went to hell, when I was going there every day. I can't say I miss it, only that I feel like I could benefit from going back.

Before the pandemic, I was going out only rarely, ordering delivery groceries, and buying most of my shit from Amazon. Now, I go out only rarely, order delivery groceries, and buy most of my shit from Amazon.

I just placed a grocery delivery order today, and I'm expecting a package from Amazon later. I thought about weaning myself off that site, but... nah.

I will continue to wear this mask in public, regardless of what diseases may or may not be circulating.

Yeah, I need to stop making promises.

I probably would have traveled more, but even that would have led to me being, right now, sitting here at home wishing winter would end already because fuck, I've had it with winter.

You know how stores keep stocking holiday items earlier and earlier every year? Well, "I've had it with winter" is now my default state, year-round.

Hm. One thing that might be different. I might not be so completely, utterly done with approximately half of the population of the US.

Even if that had been the case, I'd be completely and utterly done now.

I might still have some tiny thread of hope for the future.

Let's see... nope. All gone.

5 Like • Comment • View 1 comment

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