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 8 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 10 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.

July 10, 2020 at 12:01am

#987703

Catfall

You want me... ME... to venture... shudder... outside?

PROMPT July 10th

Go somewhere outside or where you can observe the happenings of the world beyond the walls of your home (looking out a window is fine). Spend at least five minutes watching and listening. What do you see, hear, and smell? Where does your mind wander when you sit quietly?

My housemate's cat was resting peacefully on the edge of the deck around sunset. Contented in the fading last light of afternoon, she rolled over in her sleep, and...

Well. You can imagine.

The cat's fine, of course. While it's not true that cats always land on their feet, she's just a little thing and she landed in a soft spot. Consequently, it made me laugh my ass off.

Yeah, I was outside. I joke about staying indoors all the time, but in the heat of summer, I like to sit on my deck with my laptop. Thus, I'm outdoors even now that it's midnight and the mild breeze from the inky blackness has cooled things off to just above indoor temperature. I'd expected the sharp trill of cicadas this summer, but no, all I hear are the trucks rolling by on the interstate, and the occasional friendly bump in the night.

But I like the heat of day. I like it better when the sun isn't in my face and I can see the screen better, but I'd be perfectly content with a lifetime of days between 75 and 95 F like these past few days have been. I'd even allow it to rain on occasion, but preferably while I'm asleep.

Guess I should move to Hawaii, huh?

Admittedly, it's preferable for me to have an air-conditioned indoors to retreat to on occasion, which is what I have now. But I certainly refuse to complain about the heat after suffering through sub-freezing temperatures in the winter.

But the cat's fall felt to me like a metaphor. There you are, happy and relaxed, and then you perform some seemingly innocent action like rolling over in your catnap and, next thing you know, your claws are scrabbling for purchase on the rough wood, purchase that they are doomed never to find, and then you're falling, falling.

Hopefully you land on your feet, but there's no guarantee.

There never is.

13 Like • Comment • View 11 comments

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