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:

Writer_Mike

about 8 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

a day 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

Sep 21, 2024 at 6:46am
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

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

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

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
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.

March 22, 2023 at 10:30am

#1046836

The Best Offense

There are a few more prompts for me to pick from at random in this incarnation of "JAFBG"

[XGC]. This is one of them:

Tell us about a time when someone else's humour offended you.

I gotta admit, this is a tough one. I'm not one to get offended at a lot of things, and most of the things I do find offensive aren't jokes. Like when someone doubts that I know how to drive a manual transmission vehicle. Dude, I was driving a four-speed truck around the farm at 12, as soon as I could reach the pedals and see over the dashboard simultaneously, and my first five vehicles were all manual. I only drive an AT now because a) "standard" isn't standard anymore, or much less expensive, and b) back problems make it difficult to clutch on a regular basis. But I promise you, if I wanted to steal your piece of shit car, your stick-shift isn't going to deter me.

Certainly, general things exist that offend me. Censorship, for example. One of the things I like about this website is that we're not censored, only content rated. You want to write scat torture porn? Go right ahead. It's probably going to be XGC, but nowhere are you guaranteed an audience.

But I don't much like to talk about the few things that do offend me. This is because trolls tend to use it against me. Like, let's use a fictional example. Say I'm offended by, I dunno, birds. If someone feels like trolling me, that would give them a hook to do so. They could send me pictures of birds, leave dead birds on my doorstep (don't do that; it's my cat's job), sign me up for the Audubon newsletter, whatever.

Which brings me back around to jokes.

Now, this is where I wish we had better graphics capability here. Picture a 2x2 grid, like a Punnett square

in genetics. Along the top you have the joker's intention: "Meant to offend" and "Didn't mean to offend." Along the side you have the recipient's attitude: "Doesn't look for offense" and "Looks for offense."

Now, as with the biology behind the Punnett square, in reality, things are more complicated, nuanced, and shaded, but I feel like these are the main categories. Let's look at them one by one.

"Meant to offend" x "Doesn't look for offense" - the recipient might not even realize that the joker was trolling, and might even be inclined to give them the benefit of the doubt. This, hopefully, takes the wind out of the joker's sails.

"Didn't mean to offend" x ""Doesn't look for offense" - usually not a problem.

"Meant to offend" x "Looks for offense" - oh, boy, is this wonderful for the joker/troll. They got exactly what they wanted: a rise out of the listener/viewer.

"Didn't mean to offend" x "Look for offense" - once called out, the joker will probably be apologetic. But it won't matter, because they'll be smeared all over social media for their inadvertent offense, even if they apologize afterward.

Whatever the case, the best way to handle these situations is to not assume the worst of the joker. If the person is particularly offensive, a simple explanation of why they're being offensive is a good way to start. Like "Hey, look, some people might take offense at your suggestion that we should run over bicyclists when they're on the road." If they continue to make jokes about scoring points for hitting bikers, then you know they're trolling and should be shunned.

Well, I've already banged on long enough, and I still can only remember one time when a joke actually offended me. As it was offensive to me, and not funny, I don't remember many of the details, but it went something like: a missionary knocked on a door, and an atheist answered. The missionary calmly told her about Jesus, and she went to slam the door in his face, but something kept the door from closing. She went to slam it again, still wouldn't close. Finally, the missionary said, "You might want to move your cat out of the way."

Like I said, not funny. But the way it was told (again, I can't remember it exactly) was in the standard format of a "joke." But look, I've been studying and practicing humor for decades, and I can't find anything funny about this. Is it an example of what passes for humor in evangelical circles? I know some evangelicals, and they have a sense of humor, so I don't know.

Is it trying to say that the atheist is blind to what's right under their noses? If so, they've got that backwards.

Is it a rag on cat people? That's one of the things that can offend me, so it's not only not funny, but deliberately hurtful.

Not to mention that jokes about hurting animals aren't funny in the first place.

But like I said, no point broadcasting my reaction for all the world to see (until now, when it becomes relevant as the response to a prompt). Just file it under "reasons not to engage with door-to-door religion vendors."

1 Like • Comment • View 3 comments

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