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:

Turkey DrumStik

about 9 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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

October 23, 2018 at 12:12am

#944009

Pod People

https://www.npr.org/2018/10/21/654426576/cant-find-an-affordable-home-try-living...

I'm always amused at how pictures of this sort of thing always present a pristine living space. Looks nice, doesn't it? Almost inviting.

I've sometimes wondered if a lot of domestic problems are caused by people needing their own living spaces to look like the ones in magazines.

I wouldn't know, though, because I've never tried to be that thorough in cleaning or organizing. Takes too long, and then entropy takes over and you just have to do it again and again. I dislike repeating tasks; that's why I learned computer programming. I thought that once I retired, I'd have more time to pay attention to my living space, but no - it turns out it wasn't a matter of available time, but a personality defect. Like the time I thought I only ate fast food because I was too depressed to bother cooking and cleaning up after cooking, so my doctor put me on antidepressants, which only made me eat more fast food and suffer side effects from the antidepressants. I asked her if there was a pill to fix laziness, and she laughed like I was making some kind of joke.

Anyway. I've been saying for years that the solution to the high cost of housing in these areas would be communal living, but oh no, can't have that, so they zone against it. Understand, living in something like that would be a nightmare for me, but I do realize that most people aren't introverts. The tiny house thing unnerves me as well - there is no fucking way you can get me to live in something like that, even alone, for more than a night or two.

But then, I'm financially comfortable and not faced with finding my way in a world spiraling into oblivion. So good on them for finding something that works. I think one of the stupidest things we've ever come up with as a society is the idea that we should work in one place and live in another, and spend half your day commuting between the two. What rocket surgeon came up with that nonsense? Car manufacturers? Live where you work. Arrange society so more people can do this.

Still, I'd love to see a picture of one of these spaces after a bunch of unrelated people have been crashing there for a month. Hell, even a week. I guarantee you I'd see hard evidence of the tragedy of the commons.

1 Like • Comment • View 2 comments

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