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.

May 6, 2022 at 12:01am

#1032024

Bore-dumb

They've identified the most boring person in the world, and miraculously, it's not me.

World's most boring person discovered by researchers

Now, it's not like these researchers looked at every one of the 8 billion of us and ranked us by boringness. No, it was the traits that they identified. I have some issues with the methodology, but whatever; this is for fun. Because I wouldn't want to be perceived as boring.

The most boring person in the world has been revealed by University of Essex research - and it is a religious data entry worker, who likes watching TV, and lives in a town.

Or, alternatively, it could be a researcher who studies boreology.

Incidentally, how does one become a religious data entry worker? Oh, wait, they mean they're religious AND a data entry worker.

Also, I think they left out "vegan."

The study into the science of boredom has uncovered the jobs, characteristics, and hobbies that are considered a stereotypical snooze.

"The study into the science of boredom" has got to be the most boring thing I've ever heard of.

After examining more than 500 people across five experiments researchers found the blandest jobs are seen as data analysis, accounting, cleaning and banking.

Oh, okay, so it's subjective, based on peoples' preconceptions. None of those jobs are inherently boring. You know what's boring? Security guard. Well, 99.9% of the time; the other 0.1% of the time your adrenaline really pumps. Or so I'm told.

The paper – published in Personality and Social Psychology Bulletin – also discovered the dullest hobbies were seen to be religion, watching TV, bird watching and smoking.

Religion: Not a hobby. It's an identity. Fishing is a hobby. Stamp collecting is a hobby (and a mind-numbing one at that).

Watching TV: Not a hobby. It's just something you do. Passive. Hobbies are at least somewhat active. Even fishing.

Bird watching: Okay, that's a hobby. Boring? Less than fishing. Definitely less than golf.

Smoking: COME ON.

The study also showed that being perceived as boring likely conveys low competence and low interpersonal warmth.

I have another article in the queue, which will come up at some point, that presents a different take on this.

Those perceived as boring may thus be at greater risk of harm, addiction and mental health issues.

At which point they'll be less boring, won't they? Still shunned, though.

The top five most exciting jobs

1.) Performing arts

2.) Science

3.) Journalism...

So says an article by a journalist about scientists. I bet if an accountant did the study and wrote the article, they'd find journalism and science way more boring than accounting.

The top five most boring hobbies

1.) Sleeping

2.) Religion

3.) Watching TV

4.) Observing animals

5.) Mathematics

Again... how are these hobbies? Seriously, sleeping as a hobby? What the nocturnal fuck? Everyone sleeps.

Everything about this study is suspect, in short. The interesting part is how people seem to avoid, shun, and ostracize those who are seen as boring -- as if the only true measure of a life is how exciting it is. Perhaps, to venture into the even more suspect ground of evolutionary psychology, this is some holdover from when excitement meant dodging saber-toothed tigers and hunting mammoths.

Or maybe some of you can only dream of living a boring life, and they're just jealous of those of us who can.

Yeah. I'm going with that.

3 Like • Comment • View 6 comments

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