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!

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').

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.

June 19, 2019 at 12:18am

#961125

If Dreams Are Like Movies...

Which 'semi-famous' Hollywood star would you like to meet? Why? When I say semi-famous, I don't mean a major film star. I mean someone you've seen in several movies, but never in a starring role. So no Matt Damon's or Sandra Bullock's please. Example: I'd love to meet Michael Pena. I've seen him in a lot of movies, he's a good actor, would be nice to meet him, talk to him and learn how he came into acting. Would also like to know his interests and hobbies.

By the way, I have met Michael Flanagan (Director and writer of Oculus), and Katee Sackoff (starred in Oculus, and was Captain Starbuck on the 2004 Sci-Fi version of Battlestar Galactica. Sadly, I didn't really get to talk to them, since I was their server while working in a small micro-brewery.

Wait, Katee Sackhoff is into craft beer? Well, now, that elevates her from "kinda want" to "massive crush." Consequently, I'd have to go with Katee Sackhoff. Though she played a villain in The Flash who was over-the-top melodramatic. I mean, the chick in that show was hammier than a Smithfield smokehouse.

Okay, but seriously, I don't get the whole wanting to meet celebrities thing. I mean, I guess it kinda worked out for Adam Duritz?

Story goes that this song was an ode to actress Monica Potter, and after it was released (20 years ago, gods help us all), Adam (the lead singer, with the dreads) actually managed to hook up with her for a while. Not sure if it's true, because I can't be arsed to follow Hollywood gossip. Only reason I know about it at all is that Adam Duritz is a fucking genius, and this song in particular is brilliant, so one day I decided to track down its genesis.

So I throw my hand into the air and it swims in the beams
It's just a brief interruption of the swirling dust sparkle jet stream
Well, I know I don't know you and you're probably not what you seem
But I'd sure like to find out
So why don't you climb down off that movie screen

Anyway, I don't generally engage in celebrity-worship of any sort. There are people I admire, but sometimes when you meet your heroes, they turn out to have feet of clay, as it were. I'd rather maintain my illusions.

And yet, if I bumped into Duritz on the street (or at LAX like my friend Mike did once), I'd have to at least say "thank you." But movie stars? Between all the make-up and acting ability, combined with a minor case of face-blindness that I have, I'm not even sure I could pick one out of a crowd. Nah - stay on that movie screen, and we'll be fine.

If dreams are like movies, then memories are films about ghosts
You can never escape, you can only move south down the coast

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