Complex Numbers (Book)

Blog Calendar

◄ March ► 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:

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 27, 2023 at 10:06am

#1047040

On the Bias

A prompt for "JAFBG"

[XGC]...

What's your opinion on bias in the media?

There's not enough of it.

Allow me to explain before jumping on me:

Every media outlet, indeed, every individual, has bias. Some of it is conscious; some of it isn't. With media outlets, some of them have an obvious slant in one direction or another. Others attempt to be neutral, though even choosing which stories to run shows some bias.

And it's in that attempt to be neutral that, sometimes, you run into problems.

Let's take a possibly extreme, fictional example. I'm totally cribbing this from Superman:

Say there's an independent scientist who discovers that the planet's about to blow up. He brings this to the planetary council. The planetary council, who all have a vested interest in the planet not blowing up, ignore his findings despite overwhelming evidence. So he takes it to a nice, objective, attempts-to-be-unbiased news distributor, presenting all of his scientific evidence and his argument for why the planet is going to explode.

The media outlet promptly checks his story with the council, which scoffs at the very idea. So the journal, in an attempt to cover "both sides of the debate," meticulously prints the opinions of the independent scientist, who had evidence, and the council, who basically just don't want the planet to blow up (not that I blame the council for that).

This gets out to the average Kryptonianmedia consumer, who probably doesn't understand all the science involved, and pretty soon the planet's divided in two parts (for a few days before being divided into a billion parts): one, we trust the scientist because he presented decent evidence, and two, we trust the council because, well, because they're the council, I guess.

There are the inevitable follow-up stories, interviews with the folks on the street. "What do you think of the claims that the planet's about to blow up?" "I think we should take this seriously." Or, "I think it's a load of hogwash" (Or whatever the inhabitants of that planet used to clean their equivalent of pigs.) (Yes, I know that's not where "hogwash" comes from.)

So, here's the problem with those media outlets: they're treating informed, scientific findings with the same weight as uninformed, wishful thinking, which in turn acquires the same weight as the blithering of anyone who has a vested interest in the matter.

Now that I think of it, maybe this was the real reason Clark Kent became a reporter.

But I digress. The point is that, in their attempt to be perfectly fair and unbiased, the news outlets did their planet a disservice, resulting in the planet blowing up and there being only one survivor (or two, or a whole bunch, depending on which timeline we're talking about... sorry, digressing again).

Now, sure, you get some old bearded guy with signs off the street who keeps proclaiming, "The world's about to end," and clearly, you either a) want to see his evidence or b) want to get as far from him as physically possible. But someone who researches this sort of thing? Maybe they have a point. Maybe ask other people who research these things, and not Bil-Bob in front of the weed dispensary. Sure, scientists can be wrong, but the ones to make that assessment are... other scientists, not politicians or social workers. Or, for that matter, journalists.

All of which is to say that if you have an article about how the Spring Solstice happens because of axial tilt, don't think you have to interview a flat-earther for an "alternative viewpoint."

5 Like • Comment • View 2 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.