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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 13 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 15 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.

May 22, 2020 at 12:03am

#984083

Warped

What are these "feelings" and "emotions" of which you speak? They are illogical.

PROMPT May 22nd

Music often has the ability to remind us of old memories. In your entry today, be inspired by a specific piece of music or a musical instrument. What feelings/emotions does the music or instrument stir in you? Share a specific memory your chosen song or instrument reminds you of.

I strongly suggest that you skip to about 1:15 in the following video, to avoid a good bit of cringe. Yes, I know there's sorcery you can do with the URL to make a YouTube video start at a given time, but I can't be arsed to figure it out.

I'm choosing this one because I just found it today. Really, I could have picked any number of different tunes. This one, though... whenever I hear that opening fanfare, I smile. I can't help it. It's like when my cat does something unbearably cute, or when some asshole gets karmic justice that they deserve. (I'm a complicated individual.) It always makes me think of watching the episodes for the first, second, third, or whatever time, on the living room floor when I was a kid.

Star Trek, in its many incarnations, has been a part of my life for, well, all of it. At least the parts I can remember. It began the same year I did, but by the time I had any experiences that I really remember, it had already been cancelled. But, as it lived on in syndication, I grew upspent my childhood watching reruns.

Thus, I was just the right age to actually appreciate the Animated Series when it came out, and then old enough to cringe at the obvious pandering that was Wesley Crusher in The Next Generation. I was one of those idiot kids who actually wore a Command-track shirt (the yellow one) to the screening of The Motion Picture. I collected the books and comics. Okay, no, I never went to a convention; those people are weirdos.

I do have to admit I never finished watching Voyager. It just never worked for me. But the rest of Trek, even the movies that people bad-mouth? All of that.

The kicker is, I can't even identify what, specifically, it is about Star Trek that I like so much. I'm that way with a few things, songs, shows, movies or even video games. It's not that I couldn't communicate it if I figured it out; it's that I can't figure it out.

I guess I'll just have to keep watching until I do.

5 Like • Comment • View 5 comments

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