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

October 19, 2024 at 9:39am

#1078576

But What I Want Is Cheesecake

A Guardian article from earlier this year promotes a "radical" idea.

The radical practice of eating what you want

Or, as I call it, eating.

‘Intuitive eating’ is an anti-diet that helps reconnect us to internal cues. But how does it work?

Well, first of all, if it's intuitive, then you don't need rambling "how does it work" articles, now, do you?

Figuring out what to eat is complicated. What are you in the mood for? What do other people in your household want? What can you afford? What do you have time to prepare?

Wow. If that's complicated, I hope you never have to be a writer working on a deadline. Oh, wait.

Add the ambient pressure of a culture that loudly celebrates certain foods, bodies and lifestyles as desirable while vilifying others, and the simple question of what to have for dinner becomes fraught.

Oh, but it's even worse than that when you add in vegans, gluten-avoiders, the allergic and the "allergic," religious restrictions, etc.

Recently, there has been renewed interest in an approach called “intuitive eating”, based on the idea that your body already knows exactly what it needs.

Yes, it absolutely does, and apparently, it "needs" to be overweight.

Apparently, though, that's an expected result of intuitive eating. Just try telling that to my doctor.

She recommends people ask themselves questions like: what does it mean for me to feel healthy? Am I taking into consideration my mental health, emotional health and relational health? Which of my beliefs come from accurate, scientific information – and which come from movies, TV shows or ads in magazines?

Well, I'm not going to argue with this. It parallels my feelings about drinking.

Given how emotional this work can be, experts recommend working with a professional when possible.

Again... this kind of nullifies the "intuitive" part.

Giving yourself permission to eat what you want may involve wrestling with how your culture’s foods might have been villainized by mainstream, white American culture, Johnson explains.

Oh, give me a fucking break. I get that it's fashionable to turn mainstream white American culture into the Bad Guy, but how about doing it by ragging on deep-fried butter with mayonnaise, or whatever culinary abomination came out of some Midwestern state fair this year?

Also not mentioned: the overwhelming amount of privilege it takes to "eat what you want." You think our distant, or even not-so-distant, ancestors were able to put together a shopping list or order from Instacart, like I do? No, they hunted or gathered whatever was available that week, or, later, were mostly restricted to plants and animals suited for domestication. Eating what you want is largely an industrial-age possibility, a product of privilege, and this includes veganism or gluten avoidance.

My point being that, as much as I distrust unsupported evolutionary arguments, I don't think we evolved to eat what we want, but to eat what was available, and sometimes, there wasn't a lot of that.

On the other hoof, a lot of people back then didn't live very long, so it's hardly an ideal to strive for.

4 Like • Comment • View 4 comments

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