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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Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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

Nov 14, 2024 at 12:10pm
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.

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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.

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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

January 8, 2019 at 12:20am

#949146

Who is Waltz?

How is your online persona different from your real world persona? How much attention do you pay to your personal privacy when communicating with others online?

I'm funnier online.

Mostly, this is because I have some time to think about jokes before I post them anywhere. Partly, it's because I have some social anxiety. Not enough to be crippling, but enough so that I'm a bit guarded with people I don't know very well.

Don't get me wrong; I like meeting people and socializing. Booze helps, as it does with many things. I'm just more comfortable with technology, usually.

Still, what you see here is pretty much what you get. With one caveat: like I said in a previous entry, I'm a bit of a chameleon, altering my persona based on the people I'm with. While I've rarely done stand-up comedy, I like to think of this as reading the audience. That's one thing that's actually easier for me to do in person; here on the internet, I have to imagine the audience and their possible reactions, while in person, I can see instantly when someone is bored, relaxed, attentive, or judgemental. Or whatever.

As for personal privacy, the truth is, Robert Waltz isn't my legal name. I don't use it to hide, necessarily, or to escape responsibility for what I write; it's part of the long literary tradition of pen names. But because my actual name is unique - I mean, literally unique; I'm the only one out of 7 billion+ people with my particular name - it would be too easy for someone with ill intent to find out enough about me to cause problems.

That said, I don't worry about that too much. I've been hanging around the internet for 25 years or so, and the only time anyone's ever scammed me has been when I've used credit cards in person. I don't think I'll ever understand why some people are wary about not using credit cards online, but think nothing of handing one to a restaurant server to take away and do Dionysus-knows-what with.

I will add one other thing - I've met many people from Writing.com, and if I'm meeting someone in person, I don't hesitate to use my real name. I'm not trying to con anyone, myself, and the least I can do to demonstrate this is to be up front about who I am. In return, I have to trust that they'll keep my real name off the internet. It's purely a matter of protecting myself from possible online scammers.

So, I'm just me, the same combination of faults and virtues as anyone else, but never actively trying to con anyone. Maybe one day I'll explain how I chose my pen name. But today is not that day.

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