Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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

September 6, 2021 at 12:02am

#1016860

Shut Your Pi Hole

Yes, this article is about math. Sort of. There's very little actual math involved, so no one's head should explode if you click it.

New mathematical record: what’s the point of calculating pi?
The famous number has many practical uses, mathematicians say, but is it really worth the time and effort to work out its trillions of digits?

I mean, really, when it comes right down to it, what's the point of doing anything? Why don't we just sit here and let shit happen to us, passively? Why climb Mount Everest? Why do research at the South Pole, why swim across the Atlantic, why break speed records, why build faster computers?

Swiss researchers have spent 108 days calculating pi to a new record accuracy of 62.8tn digits.

Okay, wow, that's a serious lot of digits.

It’s an impressive and time-consuming feat that prompts the question: why?

Because it's what we do if we're not uncuriously ignorant.

Jan de Gier, a professor of mathematics and statistics at the University of Melbourne, says being able to approximate pi with some precision is important because the mathematical constant has many different practical applications.

That's great. Even if it didn't, it would still be a good thing to do, as the impractical also has a purpose.

In maths, pi pops up everywhere. “You can’t escape it,” says David Harvey, an associate professor at the University of New South Wales.

This is true. It even shows up in basic cosmological equations.

“I can’t imagine any real-life physical application where you would need any more than 15 decimal places,” [Harvey] says.

This is also true. At least for now. Things have a way of expanding to require greater precision.

Given that even calculating pi to 1,000 digits is practical overkill, why bother going to 62.8tn decimal places?

De Gier compares the feat to the athletes at the Olympic Games. “World records: they’re not useful by themselves, but they set a benchmark and they teach us about what we can achieve and they motivate others.

And sometimes, by achieving something like that, you discover new methods and other things -- some utilitarian, some not.

There is no such thing as useless knowledge. Everything is connected to everything else, and just because none of us can see the Big Picture, that doesn't mean that someone, somewhere, won't make a paradigm-shattering discovery just by playing around with what us ignorant shitheels call "trivia."

It's great to ask "why" in most circumstances. But when it comes to wondering why we should learn new things, push limits, search for new ways of looking at things... well, in those cases, it's perfectly acceptable to shrug and answer, "Because." Knowledge is its own justification.

9 Like • Comment • View 5 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.