Complex Numbers (Book)

Blog Calendar

◄ May ►
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:

Adherennium Plotting something

about 2 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

2 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.

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

May 23, 2024 at 10:01am

#1071563

Across the Sea

Appropriately from Atlas Obscura, the tale of a great world explorer:

The First Viking Woman to Sail to America Was a Legendary Traveler
Back when the Icelanders called a part of Canada the “land of grapes.”

Now, it's possible that we shouldn't be using the word "Viking" like that, as I mentioned long ago here: "The Once and Future Viking"

. But I'm just quoting the article here.

Her full name, in modern Icelandic, is Guðríður víðförla Þorbjarnardóttir—Gudrid the Far-Traveled, daughter of Thorbjorn.

I'll just note here that some of those weird-to-us letters used to be in English, too.

She was born around 985 AD on the Snæfellsnes peninsula in western Iceland and died around 1050 AD at Glaumbær in northern Iceland.

Just looking at that, one might conclude that she didn't travel very far at all.

What little we know of her comes from the Saga of Erik the Red and the Saga of the Greenlanders. These are collectively known as the Vinland Sagas, as they describe the Viking exploration and attempted settlement of North America—part of which the explorers called “Vinland,” after the wild grapes that grew there.

A few entries ago, some article said that meant "Land of Wine," which may be inaccurate, but I like it better anyway.

Also, they freely mix fact with fiction. Their pages crawl with dragons, trolls, and other things supernatural.

How else are you going to scare the kiddies into behaving?

But the central tenet of the sagas has been proven by archaeology: In the 1960s, the remains of a Viking outpost were dug up at L’Anse aux Meadows, on the northern tip of Newfoundland.

I wouldn't say "proven." "Supported," maybe. It's not news anymore that Scandinavians made it to North America long before Italians did.

Among the rubble was found a spindle, used for spinning yarn, which was typical women’s work and thus possibly handled by Gudrid herself.

Right, because Gudrid sounds like the kind of chick who would do "typical women's work."

And in the Saga of the Greenlanders, Gudrid is called “a woman of striking appearance and wise as well, who knew how to behave among strangers.” That’s a trait that may have come in handy when dealing with the Native tribes of North America, whom the other Vikings dismissively called skrælings (“weaklings,” “barbarians”).

As I've noted before, who's the "barbarian" depends on who you're asking.

The article continues with a summary of the sagas involving Gudrid, and while I'm sure the originals (well, the original written-down versions, I mean) would be fascinating, the Cliff's Notes here seem to provide the pertinent details.

Another story from the sagas that has mystified readers for centuries because it mentions two “Gudrids” and has traditionally been dismissed as a ghost story could in fact be the earliest recorded conversation between a European and an American.

And no, they didn't discuss trade agreements or war. Or much of anything, considering they apparently didn't have time to learn each other's languages.

There's a lot more at the article, but as it notes, her relatives Erik and Leif got all the PR, but they didn't travel alone.

3 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.