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:

Annette in France

about 11 hours ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

about 15 hours 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

about 15 hours 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

about 20 hours 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

about 21 hours 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

about 21 hours 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

a day ago
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

Cubboo!

a day ago
In response to "Get Baked"

Yes! I discovered this a few years back (slitting the potato about 1/4 - 1/2" lengthwise, then one or two slits across the longer slit.) It came out wonderful! It seems like this was called an English jacket potato, or something like that.

2 Like

Annette in France

a day ago
In response to "Get Baked"

I'll try your oven baked potato in winter when it's sensible to run the oven for 90 minutes.

2 Like

May 21, 2024 at 7:17am

#1071456

Habit Your Way

Here's a book ad disguised as a self-help article from GQ for me to snark on.

How to Kick Your Bad Habits (And Why That's More Important Than You Think)
Plus: Why goals don’t work, and why your to-do list is wrecking your ability to do anything.

Hey. HEY! You're doing it wrong. Send me money and I'll tell you how to do it right! Until the next guru comes along to tell you that you're still doing it wrong.

A few years ago, we reached peak you're-doing-it-wrong with a video on how you're opening a banana from the wrong end. Since that, I've felt free to ignore any attempts to convince me I'm doing anything the wrong way.

You might not spend much time thinking about your habits. They are, after all, mindless.

No, they're really not. They may be comfortable, but they're not mindless.

James Clear, on the other hand, has made something of a living on it.

Lots of people make their living preaching that "you're wrong and the only way to be right is to follow me and give me money." Some of them are literally called preachers. It doesn't mean they're right.

One of his big takeaways is a bit unsettling when you consider all the habits you’ve sworn to kick (but haven’t), and all the habits you’ve really been meaning to start (but haven’t): habits, multiplied by time, equal the person you eventually become.

I get around that by not swearing to kick or start habits. Do this, combined with accepting yourself as you are, and your life becomes simpler and happier. You won't even be tempted to give what little money you have to people who are trying to convince you that there's something wrong with you and only they can fix it.

That advice, by the way, is 100% free.

In a year, the difference between a person who does 10 push ups a day and a person who eats one bag of Doritos a day is that one person has done 3650 push ups and one person is sad.

No, the difference is that one person has sore arms and pecs, and the other person is following their bliss.

Besides, this creates the illusion of a dichotomy: while it might be difficult to eat a bag of Doritos while doing push-ups, there's absolutely nothing that says you can't do both in one day.

The rest of the articlead is in interview format, and I won't quote most of it. But at one point, the interviewer poses:

But if you think about it, I feel like we're so often controlled by sort of nudges that we aren't even conscious of.

Yes, and one of those nudges is ads.

The way I see it, if you think you want to do something (or refrain from doing something), and you continue to do (or not do) it anyway, then you don't actually want to do it, and you should respect that.

Now... this may seem hypocritical of me, since I've been on a 4+ year daily streak in both blogging and language learning. Those are habits I picked up, and sometimes I go out of my way to practice them. I'm not saying we shouldn't try new things, or improve ourselves. It's the pressure that we're somehow lacking, and we should feel bad about ourselves, that I object to.

So I make it a habit to identify that pressure when it presents itself.

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