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!

a day 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

a day 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.

October 28, 2019 at 12:57am

#968536

Unwellness

https://www.outsideonline.com/2399826/wellness-industry-lies-what-really-works

Why do I keep going back to that website? It is not aligned with my lifestyle - you can tell from the name.

However, this is an interesting article.

We've Reached Peak Wellness. Most of It Is Nonsense.

Ya THINK?

Across the country, everyone is looking for a cure for what ails them, which has led to a booming billion-dollar industry—what I’ve come to call the Wellness Industrial Complex.

Some time ago, the phrase "[whatever] Industrial Complex" became played out. Everything today relies on marketing; everything is a "*-Industrial Complex."

The problem is that so much of what’s sold in the name of modern-day wellness has little to no evidence of working.

In the entire history of selling shit, the one thing that never matters is whether something actually works or not; the only thing that affects the popularity of a product is how you can brand it.

For instance: one sure way to improve one's health is to eat more vegetables. But vegetables have a problem; they're not a "product." So they're not advertised. So instead people turn to what is marketed, which are multivitamins and supplements.

Once someone’s basic needs are met (e.g., food and shelter), scientists say that wellness emerges from nourishing six dimensions of your health: physical, emotional, cognitive, social, spiritual, and environmental. According to research published in 1997 in The American Journal of Health Promotion, these dimensions are closely intertwined. Evidence suggests that they work together to create a sum that is greater than its parts.

Step 1: Artificially create divisions within the human psyche.
Step 2: Study each arbitrary division.
Step 3: Realize that the divisions are arbitrary and call their interactions "a sum that is greater than its parts."

Unfortunately, these basics tend to get overlooked in favor of easy-to-market nonsense. That’s because, as many marketers (including in the self-help space) are fond of saying, “You can’t sell the basics.” I think that’s naive. We’d be much better off if we stopped obsessing over hacks and instead focused on evidence-based stuff that works. Here’s how to get started.

You want people to buy into evidence-based science? hahahaha.

Another simple way to think about physical activity comes from physician and physiologist Michael Joyner. “Move your body every day,” he says. “Sometimes very hard.” Based on a new study published in the online journal Scientific Reports, I’d add: try to do at least some of it outside.

No. Outside is where spiders live.

The other aspect of physical health is nutrition. Here again, the best advice is the simplest: ignore diets and supplements and, instead, just aim to cut out junk like processed and fried foods.

Everything you eat constitutes a "diet," so this is misleading. Also, no one has adequately defined "processed" for me. Lots of people swear by smoothies, for example, which, as far as I can tell, are just a bunch of whatever mixed together in a blender. Baby food, basically, only runnier. Point is, blending veggies like that is processing, and yet people who whinge about "processed" food don't get all snooty about smoothies.

The roots of a redwood tree only run six to twelve feet deep. Instead of growing downward, they grow out, extending hundreds of feet laterally and wrapping themselves around the roots of other trees. When rough weather comes, it’s the network of closely intertwined roots that allows the trees to stand strong. We are the same.

Nice cherry-picking there, hoss.

In 2010, researchers from Brigham Young University completed a comprehensive study that followed more than 300,000 people for an average of 7.5 years and learned that the mortality risks associated with loneliness exceeded those associated with obesity and physical inactivity and were comparable to the risks of smoking.

Yeah, that's interesting and all, but again, we face a marketing issue. No one - and I mean NO ONE - wants to be around someone who's lonely. That leads to a never-ending spiral of loneliness. The only way to break out is for the lonely person to somehow stop acting lonely, which might cause them to become more attractive to others, but to do that they have to be fundamentally dishonest with themselves and others. And dishonesty is a crap basis for any sort of human relationship. (You can probably get away with it with dogs.)

If the world made sense, loneliness and depression would be attractive qualities.

And when you are working on something, regardless of what it is, eliminate distractions so you can give it your full attention. An app called Track Your Happiness has allowed thousands of people to report their feelings in real time.

Use our app to avoid distractions! Sheesh.

Look, almost everyone is trying to sell you something (for the record, I am not). Sometimes the things are contradictory. This is beneficial to the sellers, because buying into one thing creates a void that you can fill by buying into another thing, and so on. Keep in mind that one of the things people are selling is religion / spirituality, as seen in a section in the linked article (the section involved has entirely too much to unpack for me to have quoted it here).

And there's nothing wrong with buying stuff. I'm a big fan of consumerism in general, because it lets me be lazy. But for fuck's sake, stop buying into "wellness" fads.

2 Like • Comment

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