Complex Numbers (Book)

Blog Calendar

◄ December ► 2023
S	M	T	W	T	F	S
					1	2
3	4	5	6	7	8	9
10	11	12	13	14	15	16
17	18	19	20	21	22	23
24	25	26	27	28	29	30
31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 5 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 7 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.

December 25, 2023 at 1:22am

#1061384

Not So Facts

Here's the thing: the Doctor Who special is supposed to magically appear on Disney+ at 12:55 pm EST today. Working backwards, then, I'll have to start drinking before that time in order to be pleasantly buzzed when it starts. Sure, it's on streaming, and I can watch it anytime, but it's Doctor Who, so that's not going to happen. Now, then. In order to start drinking before noon, it's necessary for me to get all my daily activities done early. This includes blogging. Not trusting myself to wake up early (i.e., before 10 am), I figured I'd better get this done now.

Apropos of nothing, then, because that's what happens when you pick at random from a list, we have this highly informative article from, of course, Cracked.

Four Health Fads That Are Just Research Errors

I'd call any health fad an error, research or otherwise. But okay, let's see which ones they're talking about.

We’re probably about six months from the billionaires finding out about Elizabeth Bathory and bathing in the blood of slain maidens, but the rest of us have to rely on science for our health needs.

I was hoping we'd be about six months from billionaires finding out about the French Revolution, but I've been hoping that for way longer than six months. It's kind of like fusion power, which is 20 years away and has been since at least the 1970s.

Unfortunately, the science is not as, well, scientific as we’d like it to be.

Food science? Rife with errors? Quick, fetch my fainting couch.

4. The ‘French Paradox’ Is Mostly Explained by Death Certification and Time

If you’re thinking what we were thinking, we regret to inform you that the so-called “French paradox” is not a thought experiment involving an evil twin who wears a pencil mustache and striped shirt.

You forgot the beret.

It refers to the idea that French people are all walking around eating bread and cheese, smoking cigarettes and generally being French without the ill health effects that doing any of those things has in other Western countries. This has historically been attributed to their high consumption of red wine, which has been theorized to have mysterious cholesterol-removing properties, which should have been sus from the start because if wine was magical vitality juice, every fiftysomething mom would be Bruce Willis in Unbreakable.

I knew someone who bought into the "red wine" thing, hook, line, and sinker, to mix metaphors beyond recognition. He chugged a gallon of the stuff a day and, as you might imagine, it wasn't the good stuff. No idea if he was buried or cremated.

It turns out, however, that there’s plenty of deaths from cardiac and other cheese-caused events in France — they’re just not reported.

So, I guess no one cœur.

... sigh. One of my other daily routines is learning French. I should stop making puns in that language until I learn more.

Seriously, though, as someone who lives an alcohol-positive lifestyle: drink if you like it, not because you think it's some sort of medicine.

3. The ‘Small Plates’ Guy Was Fired for Fraud

If you’ve ever furtively glanced at the weight-loss tips on the back of a container of low-fat ice cream as you slowly eat the whole thing, you’ve heard of the “smaller plates” theory. It comes from a study that claimed people eat more when using larger dishware, therefore using smaller plates will trick your brain into being satisfied with less food because we’re all apparently some kind of caveman baby person.

I quit eating ice cream (except very rarely in a restaurant) long ago. This wasn't for health reasons, or because I don't like it, but on general principles; they started sneakily reducing the quantity in a container to trick people into thinking the price hadn't gone up. Not to mention using the absolute bare minimum of actual "cream" to be legally called "ice cream." You think (I hate portmanteaux in general and this one in particular, but) shrinkflation is a new thing? Ha.

Eighteen of his papers were retracted, one of them twice, including the one that claimed people ate more pasta from larger bowls. Subsequent research has confirmed that our tummies can indeed tell the difference between 17 and 70 french fries, no matter how big the carton.

Still, I'd guess that eating off of smaller plates is better than the fancy restaurants who put tiny portions on enormous platters. What's up with that shit, anyway?

2. We Think Spinach Is a Good Source of Iron Due to a Scientific Misinterpretation

No, we’re not about to tell you that a misplaced decimal was responsible for the myth that spinach contains tons of iron. (Although we totally have in the past — sorry!)

As I've urged repeatedly, don't get your science from Cracked. Or do, but just don't expect it to all be true.

It turns out there was some confusion in the research of the 19th-century German chemist typically blamed, Erich von Wolff, but it had nothing to do with a decimal point. His data concerned dried spinach, but that wasn’t clear to future nutritionists.

Gotta say, this is news to me. Not that I expect it to be true or anything.

Since we haven’t yet discovered the kind of monster who eats dried spinach, they assumed he measured fresh spinach, whose iron content is pretty well diluted by all that water and flavor and stuff.

What "flavor?"

Incidentally, a competing hypothesis that I've heard is that iron levels in agricultural soil have decreased over time. Iron doesn't just magically appear in spinach (or any plant); it's taken up from the soil like every other element in a plant. Less iron in the soil = less iron in the leaf.

I have no idea if this holds any water, either. (Pun intended, because spinach is still mostly water, which can be observed when you dump six cups of the stuff into a frying pan and it gets cooked down to about a thimbleful.)

1. ‘Blue Zones’ Are Probably Just Areas With Lots of Pension Fraud

For those who aren’t familiar, “blue zones” are both a great nickname for your testicles and pockets of communities around the world that boast an unusually high number of people who live to be 100 or even beyond 110.

Ah, the inevitable dick joke.

If you really want to live to be 100, though, the true secret is to be born somewhere that doesn’t keep good records of such things and/or study up on identity theft. Presto, you’re 100!

I also assume this sort of thing whenever an article pops up about a 35-year-old dog or cat.

Whenever officials start digging deeper into blue zones, a whopping percentage of its oldsters suddenly disappears. And we do mean whopping: Japan lost 82 percent of its centenarians overnight. Okinawa isn’t even the healthiest city in Japan. If you want to adopt some part of the Japanese lifestyle, try their beer. You won’t live longer, but you’ll die happier.

Which is what I've been saying.

4 Like • Comment • View 1 comment

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.