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 7 hours ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

about 10 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

about 21 hours ago
In response to "Paris, I Guess"

Bienvenue en France.

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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

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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

December 30, 2023 at 9:13am

#1061585

I Would Like a Word

One reason for learning a different language is to learn wonderful new curse words. Or, as this bit from Cracked points out, just words we don't have in English.

6 Foreign Words to Describe What You’re Feeling Right Now

...except it's the end of December, so all I'm feeling right now is cold, and there are perfectly good English words for that.

Are you going through something right now that you’re having trouble putting into words? Feeling a little je ne sais quoi, a little pomme de terre?

Okay, that made me chuckle.

If you’re unable to articulate what you’re experiencing, that doesn’t make your emotions invalid.

It does make you want to reevaluate your writing career. As words are kinda important to writing, here they are now:

6. Saudade: Empty Sadness for What Is Lost

I never encountered this word (from Portuguese) until just over a year ago. How do I know this? Because I blogged about it: "No Geese Involved"

Unlike nostalgia, saudade speaks to a longing for something you’re sure to never experience again, which is a component of your sadness you need to acknowledge.

That's not exactly what that previous article stated, once again demonstrating that one should never get one's wisdom from one source.

5. Ilunga: Eventually Unforgiving

In 2004, linguists convened to vote on which word, in any language, is the hardest to translate.

This was before "covfefe."

The hardest word comes from the Tshiluba language from the Democratic Republic of Congo. The word is ilunga. An ilunga is a person who “is ready to forgive any abuse for the first time, to tolerate it a second time, but never a third time.”

That's... really quite specific.

4. Perendination: One Step Beyond Procrastination

Oooh, I knew there'd be something in here that could describe me.

In Latin, we have a word for putting something off for the day after tomorrow. When you do that, you perendinate, which is one step beyond procrastination. Procrastination is for amateurs.

I must insist that this word be added to English immediately. Well, tomorrow. Well... one of these days.

3. Kummerspeck: Emotional Overeating

When you’re sad — not just from saudade, but for various other reasons, perhaps resulting from your perendination or being an ilunga — the clichéd move is to grab a pint of ice cream and eat it, right out of the container.

Can't. I don't buy ice cream anymore, precisely because it's not a pint anymore. There's a word for that process, too, but I hate it.

In German, they have a word for this type of binge: kummerspeck. The -speck refers to pork fat, so the cleanest translation into English is “grief bacon.”

Praise the lard!

2. Mudita: Pleasure in Others’ Joy

If you take pleasure in someone else’s suffering, we have an English word for that: schadenfreude. Well, it’s not an English word exactly.

It is now. If English speakers use a word enough, it becomes English. How much is enough? Depends on who you ask. But saying schadenfreude isn't English is like saying kindergarten isn't English.

In Vietnamese, they call it hỷ. In Chinese, they call it xǐ. In Japanese, they call it ki. Several other languages call it mudita, which was originally a Sanskrit word and is a whole concept in Buddhism.

Ironically, Buddhism (at least from this outsider's perspective) is more focused on suffering.

1. Swaffelen: Penis Smacking

And this one, you're just going to have to go to the link to see for yourselves. Bonus: it's Dutch. Sort of.

5 Like • Comment • View 5 comments

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