Complex Numbers (Book)

Blog Calendar

◄ February ► 2020
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
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 19 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 21 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.

February 11, 2020 at 12:04am

#975252

Terrible Lizards

Anyone ever play the game with Google Translate where you put in something in English to translate to, say, Latin - and then put in the Latin to translate back to English?

The results are sometimes hilarious, and often incomprehensible. Or both.

For example, I put in "These are the times that try men's souls." The Latin it returned was: "Haec tempora quaerunt animas." Okay, my Latin is rustier than an old barge, but that seems about right. But then I put "Haec tempora quaerunt animas" into the source and asked for English.

I got, "This is the time to destroy."

Language, as I'm rediscovering while learning French, isn't usually a one-to-one correspondence of concepts. I mean, I've known this for a long time, but there's a difference between knowing and applying. Like, it's well-known that whereas in English you might say "I'm 33 years old," in French you say something like "I have 33 years." Same idea, different modes of expression, though in that particular example it's pretty easy to tell what is meant.

While comparative linguistics has been interesting to me for a long time, I've usually been too lazy to do more than scratch the surface of other languages. Still, articles like this one usually catch my eye:

https://www.bbc.com/future/article/20200116-what-happens-when-you-have-no-word-f...

What happens if you have no word for 'dinosaur'
English is the world’s dominant scientific language, yet it has no word for the distinctive smell of cockroaches. What happens though, if you have no words for basic scientific terms?

I'm not going to do my usual copy/paste of segments; I'd pretty much have to reformat a lot of words, and I just can't be arsed. But I do have a couple of general comments.

First, comparative linguistics aside, the development of an individual language is interesting in itself. Famously, English isn't shy about borrowing words from other languages, which may be one reason it's so versatile (but also one reason why it sometimes doesn't make any objective sense). In addition to simple words, like "tattoo" (from the Samoan language, apparently), we've adapted countless terms, scientific or otherwise, from ancient languages like Latin or Greek. If a concept comes along and we don't have a word for it, chances are someone will coin something with an ancient-language base; "television," for example. And then we make it our own; in the US by saying "TV," and in England by saying "telly."

Second, these concepts are coming at us fast and hard. Some inventions require their own names. Something like "starship" was easy; it compounds two simple words from English itself. But then someone invented the transistor, and, more importantly, called it the "transistor" instead of something that I can't even imagine being built up from Anglo-Saxon words. Smallswitch, maybe? But that doesn't really convey all the uses of the transistor, which also relies on other concepts the precursors of the English couldn't have known, such as electricity, electrical current, conductivity, electrical resistance, amplification, and so on. German is much better at mashing words together to make new words.

Point is, to get back to what the article was saying, we invented the word "dinosaur" from ancient languages, languages without that symbol-concept, but the original meaning is largely irrelevant to what we think of when we think "dinosaur." So other languages have, at least, two options: they can just borrow the word like English might, at which point you have someone speaking, I dunno, the Navajo language and you can clearly hear the word "dinosaur;" or you can, as the article suggests, come up with an entirely new word for the concept based on words your language already has.

Like I said, I find the whole thing fascinating, and I sometimes wish I had the time and energy to learn even more languages to feel for myself the baffling complexity of the human capacity to assign sound-symbols to concepts.

4 Like • 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.