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:

Write_Mikey_Write!

about 11 hours 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.

1 Like

Adherennium Plotting something

about 13 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').

1 Like

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.

March 27, 2022 at 12:01am

#1029527

Unmotivation

Today, I'm going to talk about something I have very little experience with.

Motivation: The Scientific Guide on How to Get and Stay Motivated

Spoiler: it's not actually scientific.

Motivation is a powerful, yet tricky beast. Sometimes it is really easy to get motivated, and you find yourself wrapped up in a whirlwind of excitement. Other times, it is nearly impossible to figure out how to motivate yourself and you're trapped in a death spiral of procrastination.

Death Spiral of Procrastination is my 80s hair cover band.

Instead, we're going to break down the science behind how to get motivated in the first place and how to stay motivated for the long-run.

For one thing, we can stop misusing "science."

So what is motivation, exactly? The author Steven Pressfield has a great line in his book, The War of Art, which I think gets at the core of motivation. To paraphrase Pressfield, “At some point, the pain of not doing it becomes greater than the pain of doing it.”

That's actually been my working definition for a while. I can only stop procrastinating when the pain of ignoring something exceeds the pain of fixing it.

This rarely happens.

What can we do to make it more likely that we cross this mental threshold and feel motivated on a consistent basis?

Something tells me the answer to that question, sadly, isn't "Drink."

You don't need much motivation once you've started a behavior. Nearly all of the friction in a task is at the beginning. After you start, progress occurs more naturally. In other words, it is often easier to finish a task than it was to start it in the first place.

This actually also tracks with my experience. Once I start writing, I write, for example. It's getting myself to start writing in the first place that's hard.

Setting a schedule for yourself seems simple, but it puts your decision-making on autopilot by giving your goals a time and a place to live.

Nah. I've been known to set schedules and then utterly ignore them. If there's no one else involved, the only person I can let down is myself, and I'm used to doing that.

It makes it more likely that you will follow through regardless of your motivation levels. And there are plenty of research studies on willpower and motivation to back up that statement.

Actually, willpower has little to nothing to do with it. See my blog entry from a couple years back: "Good Willpower Hunting"

"I begin each day of my life with a ritual; I wake up at 5:30 A.M..."

Normally, this is where I'd simply stop reading and move on to playing video games or watching shows. The concept of willingly waking up at 5:30 am on a daily basis is so foreign, so anathema to me, that it's utterly inconceivable. Hell, I sometimes don't go to sleep until then.

Maya Angelou rented a local hotel room and went there to write. She arrived at 6:30 AM, wrote until 2 PM, and then went home to do some editing. She never slept at the hotel.

6:30 isn't really any better.

Pulitzer Prize winner Michael Chabon writes five nights per week from 10 PM to 3 AM.

Now, see, that's more my speed. It should come as no surprise that Chabon is a major writer for Star Trek these days, and I like those shows.

Anyway, I skimmed the rest of the article after that. Who knows? Maybe someone reading this will find it useful. All it does for me is increase my dissatisfaction.

But not enough to do anything about it.

3 Like • Comment • View 3 comments

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