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 1, 2018 at 1:34am

#942312

The Curse

https://www.thedailybeast.com/he-won-dollar19-million-in-the-lotteryand-became-a...

Jim Hayes won the jackpot of a lifetime and spent big on Lamborghinis and Vegas gambling trips. Then his life went south and he turned to crime.

“Having money enabled me to live my wildest dreams,” he said. “But there’s a flip side. It’s the lottery curse.”

Okay, I'm just going to come out and say it: There is no fucking "lottery curse."

The Venn diagram of "people who play the lottery" and "people who make bad financial decisions" has significant overlap. That's all. It's been said that the lottery is a tax on people who can't do math. Well, that's not the whole story - it's not a question of being bad at math, exactly, but being bad with money in general. Yeah, from a return-on-spending point of view, it's a fool's game, but at some point, someone does win big. It's not a retirement plan, but it's also not exactly like burning the cash you'd spend on lottery tickets in a firepit.

Now, I'm not saying that lotteries are evil (or good) or that people who play the lottery are stupid (or smart). Those are not the issues, either. Again, it's about making good financial decisions, and that doesn't take intelligence so much as knowledge and the discipline to apply that knowlege. The guy in this article strikes me as being of somewhat normal intelligence, definitely not a moron, but not about to crack the Unified Field Theory either.

“Common sense tells you that if you win millions, your life is made—but it doesn’t always end up like that.”

No, common sense tells me that if you win millions, you need to not blow it all.

“Right before he won, he was dealing with depression and some pretty severe problems,” said Stephen Demik, a criminal defense attorney who represented Hayes on the robbery case. “But when you win $19 million, your first stop isn’t going to be a psychologist— it’s going to be a new car lot.”

And we start to see the problem right here. Not even his words - his attorney's. No, if I won the lottery (unlikely, as I don't buy tickets), my first stop wouldn't be a psychologist OR a new car lot, but a lawyer. A financial lawyer, not a defense attorney.

Just going by the article, though, I'd say it was a combination of bad rolls of the dice, and him having no financial discipline. Not a curse, unless "being unable to deal with what life throws at you" is a curse.

I've seen a bunch of articles like this lately, and they all seemed geared toward convincing us all that if you win the lottery, your life is going to be in ruins. Well, yeah, it could be. Or it could not be. You don't hear about the people who win a lottery and spend wisely, because they don't end up living in garages and robbing banks; they're on a beach somewhere in Belize or quietly going on with their lives without worrying too much about how they're going to afford their next month's groceries. They do exist. There's selection bias there on the part of reporters, and it's pernicious.

So to sum up: go into the lottery with lousy financial acumen, and you're boned. Go into it with some amount of sensibility about money, and you'll probably do okay.

Not that you're going to win it, anyway. But someone will.

3 Like • Comment • View 3 comments

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