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!

about 9 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.

June 25, 2021 at 12:03am

#1012488

Outstanding

Entry #7 of 8 for "Journalistic Intentions"

[18+]

Insomnia is just another way to brand yourself "not normal". -Black Crisis

You know, something that's been percolating in the back of my mind for a while has to do with the tension between "being normal" and "standing out."

This generally peaks in high school and diminishes thereafter, but these days, I think it continues long into adulthood.

Clothing, hairstyles, activities... doesn't matter; lots of people walk the line between being too ordinary (and thus overlooked) and too weird (and thus dismissed as eccentric).

This is bad enough when you're actually in high school. There, you're among, at most, a couple of thousand teenagers (which, when put like that, makes me wonder how anyone has the stamina to be a teacher or school administrator). Like, my high school had around 1600 students, as I recall, roughly 400 in each class. With numbers like that it's not too hard to find ways to be noticed while still being accepted in a peer group.

Then maybe you get to college or trade school, and the numbers get larger, so you have to do more to excel at something. Fortunately, by then, the burning desire to "fit in" generally starts to recede. Still, there, depending on the school, you're competing for attention with several thousand other students.

But that was the old days.

Now, you have to walk that line not just for your immediate circles, but in competition with several billion people infesting the internet. Some people can do it through talent, looks, or smarts. For the rest of us, though, we're left with Stupid Human Tricks.

Or, for those who realize that Stupid Human Tricks can be dangerous, we have to find other ways to differentiate ourselves from the vast unwashed masses. For them, there's Munchausen's.

Now, I don't mean that to imply that people who talk about their various physical and/or psychological troubles are faking it. But even if it's real, it's a way to garner attention and sympathy, and to stand out from the crowd.

I'm not going to mention any examples here, because I'm not trying to offend anyone. But I will offer a counterexample: Chadwick Bosemen, who kept his cancer diagnosis to himself (and, presumably, some close friends sworn to secrecy). Of course, he had no need to seek out sympathy for attention; he was a talented actor. Those of us who don't get to be major movie stars, though, we have to take our attention where we can get it -- positive or negative.

And I don't want anyone thinking I'm ragging on them for this. It's just human nature, and I've talked about some of my own issues in here, too. Of course, we have to watch out for those few who do fake it to get sympathy. This usually takes three forms:

Munchausen's Syndrome: Faking (or exaggerating) illness for attention
Munchausen's-by-proxy: Faking illness in another person (often a child) for attention
Munchausen's-behind-proxies: Faking illness (in yourself or others) online for attention (and sometimes GoFundMe).

Okay, yes, I totally made that last one up. But I've seen it happen.

Of all of the possible ways to beg for attention, though (getting back to the original prompt quote there), insomnia is pretty tame compared to other things you can bitch about suffering. Most people have had it at least occasionally (myself included), so it's easy to sympathize. No one is going to think you're trying to scam them out of money by faking insomnia, not like with cancer or whatever. And it's not going to scare the unenlightened, like say talking about your schizophrenia.

Bottom line is, yes, it's hard to stand out in a crowded world. And maybe I should just give up trying.

Perhaps I'll sleep on it. Because I can. Because I don't have insomnia? Get it?

Oh, never mind. Even my so-called jokes don't make me "not normal."

3 Like • Comment • View 7 comments

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