Complex Numbers (Book)

Blog Calendar

◄ March ► 2021
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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

March 8, 2021 at 12:01am

#1005993

Full Of Hot Air

Today's science lesson won't mean anything to anyone these days, but when I first found it about a year ago, it was relevant.

When we lose weight, where does it go?

Though it might one day be relevant again.

The world is obsessed with fad diets and weight loss, yet few of us know how a kilogram of fat actually vanishes off the scales.

And normally, I'd Stop Reading There. "The world" includes a whole lot of people who only wish they had an overabundance problem; not all diets are fad diets; not all weight loss is desired; not all weight loss is fat loss; and, perhaps most of all, it's not the goddamn scales that are losing weight.

But if you can make it past the stupid-ass lede, there's some decent information in there. I'd always wondered, myself, where "lost weight" actually went. I mean, there are only five means I know of to physically shed mass: pee, poo, sweat, dead skin cells, and breath. I suppose we could count "tears" as a sixth, but I've only known one person who cried enough to actually lose weight doing it, and she was absolutely no fun to be around. Or maybe it all goes into hair and disappears when we shed or cut it? Or, hey, I know, it goes into boogers that eventually get picked when hopefully no one's looking? Okay, fine, more than five. Still, which one is it? Or is it a bit of all of them?

Even the 150 doctors, dietitians and personal trainers we surveyed shared this surprising gap in their health literacy. The most common misconception by far, was that fat is converted to energy. The problem with this theory is that it violates the law of conservation of matter, which all chemical reactions obey.

That's not quite right. It's conservation of mass-energy, because mass and energy are the same entity. But only a tiny, tiny fraction of mass gets converted into energy in the body; most of it gets converted into some other substance. Also, from what I understand, "conservation" laws aren't really physical laws like gravity or action/reaction; they're observations with no known exceptions.

Some respondents thought fat turns into muscle, which is impossible, and others assumed it escapes via the colon.

It is possible to lose fat and gain muscle simultaneously, but those are entirely different processes. And I learned early on to only weigh myself after taking a great big shit.

The correct answer is that fat is converted to carbon dioxide and water. You exhale the carbon dioxide and the water mixes into your circulation until it’s lost as urine or sweat.

And we're done here. Didn't even have to slog through the entire article to find the answer. Of course, the rest elaborates on it.

If you lose 10kg of fat, precisely 8.4kg comes out through your lungs and the remaining 1.6kg turns into water. In other words, nearly all the weight we lose is exhaled.

So, basically, by losing weight we're actually contributing to greenhouse gases and climate change. Therefore, we should be celebrating fat people, not shaming them!

Every carbohydrate you digest and nearly all the fats are converted to carbon dioxide and water. The same goes for alcohol.

For the latter, lots and lots and lots of water.

The only thing in food that makes it to your colon undigested and intact is dietary fibre (think corn).

Ew! No! Gah, I can't unthink that!

So there it is. Nope, it's not diet advice. But if you've ever wondered exactly where that lost weight goes -- well, Now You Know.

3 Like • Comment • View 4 comments

© 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.