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!

about 2 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 4 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.

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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.

December 13, 2022 at 12:02am

#1041736

Three Years

On December 14, 2019, I wrote a blog entry. It wasn't a big deal at the time, just my default: commentary on something I found on the internet.

What I didn't know, didn't plan on at the time, was that it would be the first in what is, as of today, a three-year streak of daily blog entries.

I also couldn't have known that, a mere three months later, shit would change because of a global pandemic. I almost certainly wouldn't have this streak if it weren't for that; I had travel plans. In truth, I'd rather have been able to do the travel plans. I still want to visit Belgium, dammit. It's been put off due to travel restrictions, crappy airline service, and World War III.

To that end, I have another streak going: over 1200 days on Duolingo. Which, if you do the math, is longer than my daily blog entry streak. I'm very close to being done with the French course, which absolutely doesn't mean I'm fluent in French, though I certainly know more than I did three years ago.

I might try Dutch again. Learning two languages at once proved difficult for me, and Dutch is similar enough to English to confuse me. But it's one of the other languages they speak in Belgium. Yeah, I know, lots of people speak English there as well, but this way I might have some idea if someone's insulting me in a different language.

My progress is slow, I know. But that's what I get for waiting until my 50s to try to learn something new. Lots of people my age don't even bother.

At least I found out that I could do something daily. About the only thing I could do on a daily basis, before this, is breathe. Even eating didn't happen every day. The breathing thing was questionable there for a while, too, but I managed to keep doing it.

So, am I going to keep the streak going? Well, I'm not going to deliberately break it at this point. If I do manage to go abroad, I might not have the means. I'll be okay with that, because at least I'll be traveling. Then there's always the chance of the unexpected: no internet access, computer craps out, I get injured or get sick or die, that sort of thing. You'll know that one of those happened because I won't announce it in here beforehand.

Tomorrow I'll have another article to comment on, but today I just wanted to reflect on what is, to me, a mighty achievement.

7 Like • Comment • View 4 comments

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