Complex Numbers (Book)

Blog Calendar

◄ July ► 2019
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!

a day 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

a day 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.

July 20, 2019 at 12:49am

#962878

Well-Defined

Write about some of the words that were introduced in the year you were born according to Merriam-Webster dictionary by referring to the website below:

https://www.merriam-webster.com/time-traveler

Hey, a sneaky way to get us to admit our ages!

Fortunately, anyone who can do math has already figured mine out because of my constant harping about Apollo 11. So I'll just select a few entries that catch my eye.

adaptive optics: a telescopic system that improves image resolution by compensating for distortions caused by atmospheric turbulence

One night in 2017, my friend and I were sitting on his lanai in Kihei, Maui, gazing at the night sky, when a strange red-orange light appeared over Haleakala. It moved around in ways impossible for any sort of conventional aircraft. We'd been drinking, of course, so naturally, our first thought was ALIENS!

I was joking. He was not. I pointed out that the telescope probably used adaptive optics, and what we saw was the guidance laser.

The problem with ground-based telescopes, no matter how high a mountain you perch them on, is that there's always some atmosphere between the telescope and the vast reaches of vacuum in outer space. As the turbulence consists of air of slightly varying density, this has the effect of bouncing the star, or whatever, around in the image. This is inimical to the point of a telescope, which is not, as most people think, to magnify; the point is to gather light. Long exposures are your friend. Anyway, so what you do is you point a laser at the sky and use it and a computer to make very slight perturbations in the 'scope's reflecting mirror. This stabilizes the image somewhat, although it's still not as clear as a space telescope (Hubble, e.g.) But at the time, there weren't space telescopes.

The following year, I hung out with a professional astronomer for a week, and he confirmed that not only did Haleakala's telescope use adaptive optics, but it was the first one to do so. He also told me that the way the laser works is that it is just the right energy to excite the sodium ions that persist in a thin layer in the upper atmosphere, with the resulting photons being in the exact color I saw on Maui.

So, no aliens. Just the usual humdrum human ingenuity and SCIENCE, BITCHES.

lithium niobate: a crystalline material LiNbO₃ whose physical properties change in response to pressure or the presence of an electric field and which is used in fiber optics and as a synthetic gemstone

I have no personal connection to this, but I just wanted to take the opportunity to point out that padding your dictionary by incorporating terms from chemistry is cheating.

meth: methamphetamine

Except when it becomes a household word.

ngwee: a monetary subunit of the kwacha

Thanks, dictionary! That helps so much!

...(Zambia)

Oh, okay. That helps marginally more.

second world: Communist nations regarded in the latter part of the 20th century as a political and economic bloc

I'm just including this because we like to talk about the "third world," and this is a reminder that there was considered to be a "second world" at one time as well. The division was: first world - democracies; second world - pinko commies; third world - everyone else. That didn't start out as a pejorative. Language changes.

zit: a small, red, swollen spot on the skin : pimple

And this is on my list because I thought the word was newer than that; I didn't hear it until I started getting them.

An aside about dictionaries in general: I've seen some people use dictionary definitions in arguments as if that settles things. It doesn't; it only marks you as a pedant. Dictionary definitions are, by nature, concise, generally free of nuance or context. As I mentioned above, language changes, and dictionary definitions take a while to catch up.

In short, dictionaries are not prescriptive; they're descriptive. They're not the ultimate authority on the use of language. We are. Especially "we" writers. Now, it's never right to mix up their, there, and they're; but meanings do sometimes morph, or even fall out of favor, like in the "second world" example above.

Another fun thing I realized about dictionaries: they're infinitely recursive. Self-referential. They define words in terms of other words. Like, okay, when you're a kid, your parents or teachers probably showed you a picture of, I dunno, a sheep, and told you that it's a "sheep." (It's not; it's a drawing or photo of a sheep, but what makes humans interesting is the ability to nest metaphors.) That's non-recursive. But a dictionary would be like, "Sheep: (noun) 1. A medium-sized fluffy mammal with the intellectual capacity of a boulder, whose only redeeming quality is wool." To understand the definition, you'd have to understand "a," "medium," "size," "fluffy," etc. If you don't, you have to look them up in the dictionary, and behold, you find more words you have to look up.

You have to enter a dictionary with some knowledge from outside the dictionary.

Doesn't really mean anything, but I just think it's cool to contemplate.

6 Like • Comment • View 6 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.