Complex Numbers (Book)

Blog Calendar

◄ October ► 2022
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

October 15, 2022 at 12:01am

#1039232

Reformation

Wrapping up October's "Journalistic Intentions"

[18+] with a blind quote.

"It is important to start socializing the idea of reforms now—sometimes they are upon us quicker than we think."

I have no idea what this is in reference to, and I don't want to look it up to do this entry. It's called a blind quote for a reason. I'm going to go ahead and assume it's referring to something in the US, though.

Consequently, no matter to what it refers, half the country stopped reading at "socializing" and immediately dismissed anything else. "Sounds like soshulizm to me."

I considered listing some issues that might need reform here, but there are so many things in that category in the US that it might be easier to list the things that are not in need of reform.

And if I had given myself more time, I might even be able to think of one. Thing is, when something is going right, we tend not to worry about it too much. This was the case with (yes, I'm going here) abortion laws, until suddenly it wasn't going right and it became something in need of reform.

The other problem with listing the things I think do need reform is that, inevitably, listing them creates the implication of some sort of order. Like, even if I say "in no particular order," whatever I list first will stick in a reader's mind as my top priority. If I say "police" first, you'll think that's at the top of my mind, for example. And now you probably already think it's police.

It is not.

And it's not like fixing one thing would make everything else fall into place. Well, with one possible exception: elections.

But that's still not the foremost problem on my mind.

Nor is education, nor space exploration, nor even the imminent threat of nuclear war. Not health care delivery (actual health care, now that I think of it, is one thing we do right—for those who can afford it). Not animal cruelty, not the environment, not climate change, not energy, not terrorism (domestic or otherwise), not gun violence. Even the problem of homelessness isn't the top issue for me; neither is inflation. Or the looming recession. Or living wages, or the existence of tipping, or lack of religious freedom. Racism (both systemic and personal), a general lack of affordable housing, Twitter, regressive drug laws (especially the continuing illegality of cannabis at the federal level), private prisons, infrastructure rot, drought, political corruption, and far more issues are certainly important, but again, I wouldn't put any of them at #1.

No, the biggest issue needing reform right now is the severe lack of beer in my refrigerator.

Fortunately, that one's easily solved, unlike these others, and I will do so later today.

What? With enough beer, I can pretend that these other problems don't exist.

Okay, now that I'm done, I'm going to Google the blind quote.

Huh. Supreme Court term limits and related reforms.

Just goes to show that, even when sober, I can't think of everything.

3 Like • Comment • View 2 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.