Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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.

September 14, 2019 at 12:10am

#966151

Vulture

PROMPT September 14th

Today’s prompt was written by Prosperous Snow celebrating

!

It's said that beauty is in the eye of the beholder. Describe something that you think is beautiful or attractive that someone else might consider unattractive or ugly.

Your mom.

Okay, but really, yes, beauty is highly subjective, and it's not always about physical appearance.

I'll choose my favorite example: the turkey vulture

.

Those birds are, I think the vast majority of people would agree, amazingly unattractive. Ugly, even. So it's not their appearance that is appealing, or even their feeding habits - the idea of eating carrion is repulsive by any human standards.

That's why they're bald, you know. So they can stick their heads deep into a corpse without fouling head feathers. Well, the mechanics of evolution are more complex than that, but that's the general outcome of natural selection in vultures.

And yet, we humans eat carrion, also. Not, to be sure, rotting corpses; but everything we eat (yes, even if you're vegan) is dead. Fresher than a vulture's meal, perhaps, but still... dead. I mean, it's not like lions or whatever eat prey while it's still alive, but there's a brief window there between "I killed it" and "leave it for the vultures," and that window is longer for us, because we have the technology to make it so.

But that brings us to the true beauty of vultures: they remove from the environment those things that, were they to be left to rot, could easily spread sickness. They're the sanitation engineers of the animal kingdom, thus inspiring the scientific name of the turkey vulture: cathartes aura, "golden purifier." They do the job no one else will - or even can - do, and are reviled for it.

It doesn't stop there, though. Turkey vultures in particular are remarkably efficient birds. They won't even flap their wings if they don't have to, preferring instead to locate convenient updrafts and glide to higher vantage points. Maximum reward for minimum effort: I respect, admire, and emulate that. And it seems they don't fly because they have to, but because they want to. I mean, wouldn't you?

There's a popular misconception that vultures circle around animals who are near death, waiting for that moment when they can get their meal. This is not the case. First of all, no self-respecting vulture is going to start munching on a dead beast while it's still fresh enough for apex predators to get their bites in, not unless they're really hungry. Second, the circling is actually the birds staying in an updraft. Hang glider pilots like to look for vultures so they can tell where the thermals are.

They're not cute. They're not cuddly. They're not threats. They're not pets. But they are, in their own way, beautiful.

6 Like • Comment • View 4 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.