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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QPdoll

about 11 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

about 14 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

Sep 20, 2024 at 9:08am
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

October 2, 2023 at 8:53am

#1056555

Bad Influence

I've been banned as a bad influence, so I can identify with this Cracked article.

5 Innocent Things Banned as Bad Influences

I, too, was innocent.

What do you do when your citizens come upon something new? You must ban it, obviously. New things lead to new thoughts, which lead to new actions, which lead to your downfall.

Probably why it took fire so long to really catch on.

5. Syria Banned Yo-Yos, Thinking They Caused Drought

Every once in a while you hear about some country getting all panicked over a superstitious belief. Then you remember that, here, people still think floods are caused by God being angry that we let gays exist.

Looking for something to blame, the country’s holy men turned to a new toy people were playing with: yo-yos. Everyone was praying to the heavens above for rain, they reasoned, and meanwhile here were yo-yos springing to the ground below, and that surely disturbed everything.

Ha ha those idiots. Don't they know yo-yos could have been used to dowse for water?

At the time of this ban, international reports had to explain to people just what the toy was. It was an invention commonly known as the bandalore, according to dictionaries at the time, and had been called a “quiz” in England.

Which would make yo-yo tricksters bandalorians.

You may be tempted to laugh at the confused holy men. But shortly after the ban went into effect, the rains returned, so the holy men got the last laugh.

And this, folks, is exactly why we need to avoid confusing correlation with causation, or to think that because you took skunk oil and your cold symptoms lessened, it was the skunk oil that lessened your cold symptoms.

4. Germany Banned the Game ‘Risk,’ Saying It Would Induce Feelings of Militarism

That would be like the US banning Monopoly because it would induce feelings of capitalism.

3. The BBC Banned Desk Lamps

Writers with lamps would pen “smut” and “innuendo,” warned the book, inspired by the light into producing “furtive” and “degenerative” programs.

Hm... *searches Amazon for desk lamps*

2. China Banned Videos of Eating Bananas

Speaking of smut and innuendo.

In time, we came upon further banana videos that — while not porn, by any conventional definition — were so erotic that we refuse to embed them here.

I'm sure we can find them ourselves.

1. A Town Banned All Concerts When a Neighboring Lot ‘Accidentally’ Booked Rage Against the Machine

If the band performed as planned, people might be able to hear the lyrics all the way in town, residents complained, which would inspire in them all kinds of corrupt thoughts. Or maybe the thousands of concertgoers would descend upon the town and riot.

Worse, someone might... dance. Quelle horreur! After all, you know why Baptist teens aren't allowed to have sex? Because it might lead to dancing.

(Yes, I know the incident in question took place in Utah, better known for LDS than Baptists, but it's a joke.)

3 Like • Comment • View 1 comment

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