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 11 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.

February 12, 2022 at 12:02am

#1026506

Model Citizen

A quick note: My last remaining aunt suffered a stroke this week. She survived, and they think she'll even improve (remarkable considering her age), but my cousin (her son) and his wife want me to go to NYC next week to see them all anyway. So I'm going; in the Before Time, I used to visit once or twice a year, but I haven't been since November of 2019. Therefore, some entries next week will post at odd times.

Oddly enough, this is kind of related to the prompt that came up at random today from the list over at "Journalistic Intentions"

[18+]...

"The process of racial triangulation—of which the MMM [model minority myth] is a prime example—essentially places Asian Americans in a racial bind between whites and other people of color."

As usual for this month's prompts, I'm not looking up the quote for context. Which is kind of difficult to do in this case; whenever someone talks about race or culture issues, it seems important, these days, to get the racial and/or cultural affiliation of the source so we know whether they're saying something racist or not.

But I'm not doing that, so I have to take the quote at face value.

While I think that, in general, lived experience is damn near worthless when it comes to things like risk assessment ("I wasn't wearing a seat belt and I survived the wreck, so seat belts are useless"), when it comes to prejudice, lived experience is pretty much all we have to go by.

I have no known Asian ancestry, so I can't speak to the subject in the prompt except to say that this is not the first time I've heard a similar sentiment.

But I come from another (formerly) "model minority," so maybe I have some relevant lived experience anyway. Or maybe not. I'll talk about it anyway, and risk getting called names.

I pass for white, so that's how people treat me -- until they find out my actual ethnic heritage, which I don't always divulge unless it's relevant. When that happens, some people take it in stride. Others clam up and go away. Still others just can't resist making Holocaust jokes (in all fairness, some of those are pretty funny).

And some people who pride themselves on not being the slightest bit racist start talking about the Palestine situation, as if I have fuck-all to do with what the government of Israel is doing over there. I have my own views on the subject, of course, and they boil down to "both sides are bad." But it would be like if you found out that someone's great-grandfather immigrated from Tsarist Russia, and you started giving them shit about what Putin is trying to do with Ukraine.

Don't get me started on space lasers.

Which brings me to my aunt (I told you that would become relevant). No, she doesn't have a space laser, either (dammit). Her brother was the one I talked about a few entries ago, who went to war in the US Army and was one of the people who liberated Dachau, and it basically destroyed his mind.

It wasn't just him, though. My mom was the oldest; this aunt (I'll call her E for this entry) was the youngest. My mother kept her religion as best she could, marrying my father (also Jewish) but eventually ending up living in rural Virginia, hence my rare upbringing. Their other sister stayed single and devout. But E, having seen what her brother went through, renounced religion (though not ethnicity), married a goy, and went to live in the Midwest.

In that way, I take after E more than I do my mom. Hence one reason I'm close to that side of the family. Oddly enough, we never got along all that well, perhaps because we're more alike than is comfortable.

Point is, she fit in, as did her two sons (one of them lives in California, so I don't see him as often). And that, to me, is the essence of the "model minority" - the ability to fit in to the majority culture. Things go south around here, as they're doing, and no one has to know what our ethnocultural heritage is.

Other minorities are more obvious. But for Asian-Americans, I suspect that it's not about looks; it's about cultural values.

Thing is, though, racism is not "better" if you're praising the target of it. I know there's a perception that people of Asian descent do better in school, and while on the surface that seems like a good thing, it can still be tinged with a sense of jealousy and "otherness." And that might even be borne out statistically, but again, when it comes to issues like this, it's lived experience that matters.

At one point, I was at a blackjack table in Vegas, a rather attractive woman of obvious Asian descent a couple chairs away. Some drunk white guy came by and leaned over toward her. "Settle a bet for me? Where are you from?" Or some words to that effect.

"Los Angeles," she replied.

"No, no, where are you from from?"

I mean, shit, dude, she says she's from L.A., she's from L.A. Period. I'd learned prior to that to never ask that question of people who seemed to be from other cultures, because it can be perceived as rude. I'd done it, meaning it with the best of intentions, but the other person would usually go stone-faced and say something like "I'm an American, just like you." That wasn't what I was asking, but apparently they'd encountered enough prejudice that the question itself is offensive. If you're from Queens, tell me you're from Queens; then we have something in common (that's where my other aunt lived). And how did you know I'm American, anyway? The accent, I suppose.

You don't usually get that from white folks. "Where are you from?" "Ottawa."

I digress. What I'm trying to say is that it can be a minefield.

Thing is, there are racial differences. Otherwise, it wouldn't be such a touchy subject. Some of the differences are physical and thus meaningless except as an identifier; others are cultural. The problem comes in when we ascribe to all members of a culture the common stereotypes of the culture. You're Scottish? You must be frugal. You're African-American? You must love watermelon. You're Jewish? You must be stingy (never mind that this means the same thing as "frugal" but with different connotations). You're Asian? You must be pretty smart. You're Irish? You must love to drink and fight. And so on.

Honestly, I wish we could find a way to move past this "racism" thing. I think we've made some progress, but there's still a lot of it out there. It's one thing to be proud of one's heritage, it's quite another to let it fool you into thinking it makes you better or worse than anyone else. Your actions can do that, but not your ancestry or your skin tone.

There are good people and assholes in every group (except for the groups of "good people" and "assholes," of course), and I don't think it serves humanity very well to assume that every member of a group has the same values. I know people like to take shortcuts sometimes when getting to know someone, but some of those shortcuts can be hurtful.

So don't be an asshole. And if you screw up and act like one, which you probably will, accept it and apologize when someone calls you out on it.

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