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 2 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

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

February 23, 2019 at 12:30am

#952872

Insert Cat Pun Here

https://www.theatlantic.com/science/archive/2019/02/cat-psychopaths/583192/

When Becky Evans started studying cat-human relationships, she kept hearing, over and over again, about how cats are psychopaths.

First of all, cats aren't psychopaths (as the article goes on to explain). That's just more made-up bullshit, like the folk "wisdom" that a cat will "steal a baby's breath." Shit like that has led to the death and/or torture of more cats than I care to think about.

Second, there's a viral idea floating around the internet to the effect of "your cat is trying to kill you."

Stop that shit. Stop it right now.

To be sure, there are mean cats out there, just like there are mean dogs or people. But as a group? No.

Here's the problem: I've known a number of cat-haters in my life, the kind of people who, when they see a cat in the road while driving, deliberately aim for it. People who drown cats, or throw stuff at them, or shoot them. Stuff that, if they did it to dogs, they'd face a mob with torches and pitchforks, but for some reason, when it's a cat, other people just shrug it off.

Don't get me wrong - I'm not here to change anyone's mind about what animals they like or don't like. Not my business, though I could never fully trust a cat-hater. But there's a difference between not liking an animal (I'm not overly fond of dogs) and actively seeking to harm them (I never would).

And the whole "your cat is trying to kill you" meme just fuels the fire of cat-haters, making it that much more likely that they'll harm an innocent kitty. So that shit needs to stop.

Sometimes I wish that there were actually an afterlife, and your position in the hereafter is directly dependent on how well or poorly you've treated pets.

In the meantime, why don't we all try meeting other animals halfway instead of trying to anthropomorphize them? A cat gives clear signals when it wants to be left alone - at least, clear to anyone who cares to learn a cat's body language. It also makes it clear when it wants to be petted; just don't fall for the exposed-belly trap. Cats roll onto their backs to show that they trust you; tickling most cats when they do that is a betrayal of that trust. (Having said that, I do have one cat who loves to have her belly rubbed. The fur there is very soft.)

To summarize, cats aren't dogs. And neither cats nor dogs are people.

8 Like • Comment • View 3 comments

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