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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Write_Mikey_Write!

about a minute ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

Adherennium Plotting something

about 2 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

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Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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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