Complex Numbers (Book)

Blog Calendar

◄ December ► 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	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:

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

December 8, 2020 at 12:08am

#999846

Do Not Want

"30-Day Blogging Challenge ON HIATUS" [13+]:
8. Brownie Day
There are many types of brownies:
Fudgy, cakey, 'special', with or without nuts, etc...
Tell us something about brownies.

"JAFBG" [XGC]:
What is something that you honestly want for the holidays that you could never admit to your loved ones?

Okay, I gotta admit I'm not feeling it today. I can't figure how to make these prompts work. It happens sometimes. I'll respond to them straight up, but don't expect creativity, humor, or any of that shit from me today. Yesterday, and continuing into today, I was utterly overwhelmed with frustration and resentment at life, the universe, and everything, and I just don't see that changing anytime soon, which only feeds back onto the frustration in an infinite recursion.

Less than two weeks to the solstice. 5:02 am Eastern time, Monday, December 21. It's been my habit, in most years recently, to stay awake through that longest night. Somehow I always feel like the astronomical reversal could mirror a reversal in my own shitty December mood. And sometimes it does. But again, I just don't see that happening this time. It's frustrating and I resent it.

And look, concerning that second prompt up there, if I had loved ones, if I could bring myself to give enough of a shit about myself or anyone else, then presumably I could tell them anything, even including admitting something I wanted. On the other hand, I wouldn't share it here. That's not how any of this works. But when it comes to something that I "honestly" want for the holidays, it would be for the holidays to be fucking over already. I'm done with this shit. I did my usual taphouse visit yesterday, even though it was cold and dreary like December usually is, and I sat on the patio and got subjected to holiday music. Not even beer could make me feel better. I mean, seriously, how many versions of "Have Yourself A Merry Little Christmas" can they fit into a single one-hour dining experience? It was like... that song, some other song, then a different version of that song, then another sappy POS song, then that song again in yet another version, then "Baby it's cold outside," then that sonofabitching song again... it's frustrating and I resent it.

Maybe I just need to make brownies, as per the first prompt. I used to do that sort of thing, you know, like normal people: bake stuff when I felt like it. It just feels like too much work, these days. And then what? Then I end up with a bunch of brownies or whatever. I could, technically, eat them quickly, but that wouldn't be healthy. Or I could eat them slowly, but then they'll go bad before I finish them. It's frustrating and I resent it.

The problem with other peoples' brownies is you never know what you're going to get. Too many variations. I like them denser than a neutron star and completely free of nuts of any kind -- basically a chocolate bar. But you go to a restaurant or whatever and they'll have a light fluffy cakey brownie thing with walnuts and/or pecans. Look, I got nothing against nuts (apart from peanuts, which aren't really nuts), but I want my chocolate unadulterated. It's frustrating and I resent it.

But then when I've tried to make my own, it never goes right. The edges become hard as bricks and the inside is mushy as a dead rabbit. It's frustrating and I resent it.

I can't even bring myself to make a snide pun about the other kinds of brownies out there: the gnome-type ones from folklore or the girl scout ones. I want to, but again, I'm just not feeling it. I don't see a way out of this funk. I just don't. Can I just sleep through to March? Please? Oh, but then I wouldn't reach my goal of writing a blog entry every day this year. But that would be typical, wouldn't it? Most of my goals fail. It's frustrating and I resent it.

5 Like • Comment • View 9 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.