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.

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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.

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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.

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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.

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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.

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Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

December 16, 2022 at 12:02am

#1041833

Not Giving Up the Ghost

I really like ghost pepper.

A Guy Ate A Pepper So Hot That It Ripped A Hole in His Throat

I am, however, not a complete idiot. Usually.

The ghost pepper, also known as bhut jolokia, is one of the hottest chilies in existence. It scores more than one million on the Scoville heat scale, which should tell you... well, not much of anything because spiciness can’t actually be measured using numerical units. So just picture the spiciest chili you can imagine, and we’ll say this is way hotter.

There are supposedly hotter chili peppers, such as the Carolina Reaper. When I tell people I like ghost pepper, they inevitably bring that up, so I'm getting that out of the way.

Look. It's not the "heat" that makes me enjoy ghost peppers. I'm not chasing some bragging rights or trying to prove that I have balls. Even if I was ever tempted to play the macho "who can eat the hottest pepper" game or whatever, I'm way too old for that now. It's just that, in small quantities, ghost pepper adds a nice tingly touch to a lot of different foods. And drinks. Hell, I've even had a ghost pepper IPA. I don't normally like IPAs, but this one was good. Because of the pepper. It was the product of a brewery / barbecue restaurant in Tonopah, Nevada (I don't know if it's still there), and one thing ghost pepper is excellent with is barbecue.

A little bit of it is like kittens purring in your mouth.

Too much, and the claws and teeth come out.

Anyway, the point is, I do like spicy food, but not enough to actually eat a ghost pepper like a complete and utter moron.

All of which brings us to our story about a ghost pepper challenge at a California restaurant in 2016.

"Challenge" = "Dick measuring contest."

Our 47-year-old hero, whom the Journal of Emergency Medicine does not identify by name when documenting this incident, came to the restaurant and ordered their ghost pepper burger.

So, just a little bit younger than I was at the time. Come to think of it, I'm pretty sure 2016 was the year I had the ghost pepper IPA in Nevada. Not sure about that, though; these things tend to blend together.

This was not a normal menu dish but part of a contest, as the restaurant believed that most customers would not be able to stomach bhut jolokia pureed over a hamburger patty. However, our hero did down the burger.

It's also good on burgers. Again... in small quantities. What you have to do is use a ghost pepper sauce that dilutes it enough so that you can spread it very thinly on the patty, thus capturing the taste without setting your face on fire.

His mouth burned afterward, and he chugged six glasses of water, which was expected.

Now, one doesn't become a spicy food eater without, occasionally, overdoing it. It's been a while, but there's one thing I remember: water isn't going to help.

He then threw up, which was again something the restaurant likely anticipated.

Hot chilis are hot because of an alkaline compound in them. Stomachs are stomachs because there's an acid in them. When acid meets alkaline, they neutralize... sometimes explosively (science fair volcano, e.g.). Plus, enough pain will make you ralph.

But after that, he felt chest pains so severe that he needed to go to the emergency room.

This is not a normal reaction to eating hot peppers.

At times, you may have felt like you’ve thrown up so hard that you shredded your throat. But once doctors examined this guy, they discovered that he actually had torn a hole right through his esophagus — a rip about one-inch long.

And I won't be pasting the other gory details here.

We’re not calling a slashed gullet the certain result of eating spicy food, but we think the message here is clear: When you inevitably attempt a ghost pepper challenge yourself, be sure to slurp a cool milkshake between every bite.

That's not a bad plan. Beer, incidentally, as wonderful as it is, doesn't do much to mitigate capsaicin overdoses. But you know what a better plan is? Don't fucking do stupid triple-dog-dare hot pepper challenges.

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