Complex Numbers (Book)

Blog Calendar

◄ July ► 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	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:

Write_Mikey_Write!

about 6 hours 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

about 8 hours 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.

July 25, 2021 at 12:01am

#1014265

Star Start

I've thought about this one before. The perils of being a science fiction fan and sometimes a writer. From "JAFBG"

[XGC]:

You've been given the opportunity to start a new civilisation off-planet. Who is banned from joining you and why? What rules will you put in place?

The only socially acceptable answer to the first question is "fat white guys."

But since I'm a fat white guy, I won't say that. But I wouldn't ban any demographic group. I'd want as diverse a population as possible, not only for the sake of inclusion but for genetic preservation.

The only people banned outright from joining would be assholes. Why? Because they're assholes. How I'd sieve them out is a different question; I'd have to resort to psychological screenings, and of course the criteria would be known only to me to prevent cheating. Because assholes will cheat given the chance.

The assholes can stay here and inherit the Earth.

I will resist the temptation to ban "everyone except me and a wide selection of attractive females" from the journey. 15-year-old me lived a very long time ago and had different priorities, but he's still in here somewhere.

As for rules, well, as much as I'd like to be a benevolent dictator, history has shown that no matter how benevolent the dictator starts out, becoming a dictator makes you an asshole. Not to mention that there's nothing in the prompt about me living indefinitely, and whoever succeeds me will face the same problems.

No, as imperfect as it is, the only rules I'd put in place would be ones to make the civilization (US spelling here) a democratic republic. Like the Constitution of the US, only hopefully without all the baggage like the "3/5 rule." There are of course other models for democracies, but the US is the one I'm most familiar with, and as ideals go, it's not bad -- we just sometimes have trouble living up to those ideals.

Mostly because of assholes.

The essential feature of a democratic republic is to have in place protections for everyone's rights, while allowing for social changes over time. In a pure democracy, the simplistic implementation leads to mob rule. Like, say, suppose 51% of the population votes to ban alcohol. This is obviously one of the worst things that can happen to a society (that's not just my opinion; look at history again), and tramples on the rights of the 49%. Or to use a slightly less controversial example, you can't have 51% of the population say, "We're going to make it illegal to practice [insert specific religion here]."

The goal, therefore, is not to enforce the will of the majority but to protect the rights of the minority. Hence democratic republic instead of pure democracy.

There are contradictions inherent in all of this, of course. I think you'd find that whatever system of rules and government is put into place, there will always be contradictions. We as individuals can't avoid internal contradictions; the problem is only magnified when you get to the government level. The trick is to maximize freedom for everyone to the extent that it's feasible to do so.

Except for assholes.

6 Like • Comment • View 3 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.