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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Signature for those who have won a Quill Award at the 2020 Quill Awards

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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 30, 2020 at 12:21am

#989487

Thoughts for Thirty

Had a great time, y'all!

PROMPT July 30th

Congratulations on making it to the last day of the competition! What was your favorite prompt from the last month? What was the most rewarding aspect of participating in the competition?

This time, I actually went back and refreshed my memory about all the prompts from this month. My memory isn't great and I can't usually remember what I posted from more than a couple of weeks ago.

I think I had the best time with the "biased reporting" one. Not only did it give me an excuse to rant about something I like to rant about, but seeing other peoples' responses was interesting. I stand by what I said, but I still feel like I could have made it more clear or expanded on a couple of the items, especially my train of thought at the end that concluded that there probably isn't a such thing as unbiased reporting.

Everyone has a bias, but some people try harder than others to at least be fair. And by "fair," I don't mean "presenting all sides" on occasions when there really isn't more than one side; I mean presenting the relevant facts as disclosed by people who should know what they're talking about.

Anyway. The most rewarding thing was, as always, reading what other people write. I'm obviously biased and have opinions, so I'm not always going to agree with other people, but I do try to respect that other people have opinions that differ from mine, and often for good reason.

Except for the Chicago-style "pizza" thing. I'll die on that hill.

But the other thing I like about these challenges, and the other reason I keep coming back to participate in them, is because the prompts often make me think. Sometimes they make me think things I'd rather not think, like the prompt about travel, which as I mentioned is a sore spot for me right now. By the way, that's why I won't be participating in Blog Travel Month. I hope those who do have a great time, but I just can't pretend to travel during a month when I was supposed to actually travel. I don't think there's enough depressing music out there to lift my mood from something like that.

Usually, though, these prompts give me the opportunity to write stuff I normally wouldn't bother to write. I often learn something in the process. I hope other people do, too.

Thanks for reading. I hope you'll stick around. I'm not going anywhere (dammit); I have a huge backlog of stuff I want to talk about, and I'll be doing some more mini-contests.

7 Like • Comment • View 6 comments

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