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.

July 15, 2019 at 12:03am

#962636

I Can Read the Writing on the Wall

Describe a time when a personal failure became a positive experience.

Hm, so many choices. So... many... failures...

I could talk about the time I fucked up a pot roast in front of people, and discovered the world's greatest pizza when we ordered out. Or maybe all the times I fell off my bike as a kid before I finally learned to stay on (I can still stay on a bike. It's like riding a... well, you know.) Or being unable to convince Debbie to go to the prom with me so ended up with Sara (I might have changed their names to protect their reputations).

But no, I'll tell you about the time I decided not to become a newspaper photographer.

I learned darkroom skills before I got seriously into photography itself. In high school, among other things, I became the yearbook's darkroom technician because everyone else had a life. And maybe because I was the only one who knew what he was doing.

Mom got me a camera for graduation, and I took it with me to college. Joined the college newspaper and started taking pictures for them. We had to develop our own film, make our own contact sheets, and print our own photos to spec, and I was rather good at both ends of the business, including retouching the images on the fly in the darkroom.

So I thought, well, maybe this engineering thing isn't the best use of my time, and I applied for a summer internship at an actual newspaper.

In those days, that sort of thing was highly competitive, and I didn't get the position. I kept on with the college paper, though, because it kept me in beer money; eventually, I graduated and became an engineer. Still did photography on the side for a while, though. So. Many. Weddings.

Now, journalism is all but dead; photography is entirely digital; and everyone carries a camera, so there's nothing special about it. Meanwhile, engineering is still a thing that people do and get paid a decent wage for.

So, it's fortunate that I didn't get that internship. Positive experience? Sure - as an engineer, I ended up making a decent living and not having to be artistic at all. As a journalist, I probably would have found myself out of a job. The world still needs Clark Kent, but has no use for Jimmy Olsen.

Besides, it's just not the same when you don't have to play with fun chemicals to make an image.

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