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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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').

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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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

November 13, 2019 at 12:09am

#969536

To Be Honest...

PROMPT November 13th

In what circumstances do you believe it is okay to fib or tell a white lie?

What? It's never okay to fib, and white lies are lies! One should always be completely honest with both oneself and-

Oh, I can't go on like that. There's only so much bullshit I can spew at one time.

The truth is: lies keep the world running smoot- okay, less roughly than if there weren't lies.

When I was younger, I might have actually believed what I was starting to say up there, that honesty is always the best course of action. But I learned better, oh yes. All it took was one honest answer to "Does this dress make my butt look big?" and I learned. (Of course, it seems like, these days, that's the goal with clothing.)

And, of course, I am sometimes a fiction writer, and what's fiction but a lie? Sure, everyone involves knows it's untrue, hence the name "fiction," but it's still premeditated dishonesty.

Do I always tell the unvarnished truth? Hell no. But I have a few guidelines for myself when interacting with people.

First and foremost, don't lie more than you have to; keeping a story straight is hard enough when you tell the truth. I'm naturally full of contradictions and hypocrisies. Compounding those by lying about them, when you'll have to remember which lie you told to which person later, takes too much mental energy.

Second, before you lie, take a second to check yourself: are you trying to make yourself look good, or gain some advantage, or are you just trying to grease the wheels of conversation? I expect everyone puffs themselves up a little bit, but saying you've hiked across Antarctica, gone into space, or swam the English Channel when you didn't can be detrimental to your reputation. (Then again, if you've done any of these things, shut up; you're making the rest of us look bad.)

Third, rather than enumerate the situations in which it's okay to fib or tell a white lie, I will enumerate the situations in which it's not okay to do so: 1) in a committed relationship; 2) in court. That's... well, that's about all I can think of at the moment.

In short, lies make life better for everyone - up to a point, and that point is when someone gets harmed by false information. But that doesn't fall into the category of "fib or white lie."

Now, if you'll excuse me, I'm off to prepare for my hike across Antarctica.

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