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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 8 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 10 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.

February 20, 2022 at 12:02am

#1027069

I'm Game, Said the Deer

I've never been a big fan of this source, but whatever... this article seemed interesting.

How 'Gamification' of Everything Is Manipulating You (and How to Recognize It)
Companies are using gamification to manipulate you. Here's how to see it and fight against it.

"The only way to win is not to play?"

“Gamification” is the practice of adding game-like elements to non-game contexts. It isn’t new, nor it is always a negative, but it is being aimed at consumers and employees more and more frequently, whether to keep you addicted to an app, motivated at work, or inclined to spend your money on something.

And I'm usually okay with it if they're up front about it. Duolingo, for instance, uses psychological tricks from gaming to try to keep people motivated. They make no attempt to hide it. It works for me.

There’s nothing wrong with gamifying our lives. We do it all the time, like when we promise ourselves a reward for cleaning the garage, or work out extra hard to get a little higher on Strava’s leaderboards.

Who? No, I can't be arsed to look that up.

There’s nothing necessarily wrong with making consuming a product or doing a job “fun,” but when marketers and employers are hacking our pleasure centers in ways we don’t fully recognize, that’s manipulation, and that’s not really a game.

Marketers have been manipulating us forever. I rarely watch stuff with commercials, so I'm not exposed to them on a regular basis -- hence, when I do see a commercial on someone else's TV, I'm generally amazed at how blatant the manipulation is. I get the impression people who are used to it just take it in stride.

Behaviorists’ studies of rats and humans prove that both species are more motivated by intermittent, unpredictable rewards than anticipated ones.

Only rats are probably smarter about it.

I used to think Twitter just loaded a little slowly because that’s how long it took, but it turns out that it’s a feature not a bug. Twitter, Instagram, and other social media sites reportedly artificially lengthen the time between when you click on the app and when the content shows up in it as a way to increase the sense of anticipation—and keep you coming back again and again.

For whatever reason, this little tidbit -- if true; I haven't checked it out -- pisses me off way out of proportion. I'm on the internet because I want instant gratification. When I click on something, I want it to load right the fuck away, not spin the cursor. That doesn't build anticipation for me; that makes me close the window. When I get sent a YouTube video, I have a simple rule: if you spend more than 5 seconds on logo or other extraneous bullshit before getting the damned content, I don't watch. And that's me being generous; if the video is formatted vertically, I don't even give it that long.

Fortunately, I'm not on social media so I haven't experienced these supposed artificially extended load times, myself.

In any case, the rest of the article describes some other game-type techniques used to maintain engagement. As noted, not all of these things are inherently bad, but it doesn't hurt to be aware of how you're being manipulated.

I'll only note one more thing from the article:

A streak offers nothing beyond the streak itself. The longer a streak goes, the more you’ll be motivated to keep it going, mainly because breaking it would cause you some tiny amount of disappointment.

*Looks at my 26-month daily blogging streak*

*Saunters off whistling innocently*

6 Like • Comment • View 2 comments

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