Complex Numbers (Book)

Blog Calendar

◄ July ► 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:

Write_Mikey_Write!

about 8 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 10 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 5, 2020 at 12:23am

#987254

Inspiration and Aspiration

inspirational (adj.): providing or showing creative or spiritual inspiration

PROMPT July 5th

Tell us about someone you find inspirational.

https://www.lexico.com/en/definition/inspirational

Well, I've already mentioned Leonard Cohen too many times this month. I think he, more than anyone else, made me want to attempt this whole "writing" thing.

Springsteen, maybe? Nah, doesn't quite fit the definition. I can like someone's art without having it nudge me into making my own.

Neil Gaiman? Hm. I've deliberately cribbed his writing style on occasion, but I'm not sure that counts, either.

Or I suppose I could pick the person who penned this prompt, because they inadvertently inspired me to write this entry, or Emily

for posting it. But I don't think that really fits the spirit of the prompt.

The problem might lie in the definition, or in myself. See, I'm neither "creative" nor "spiritual." And I've grown to resent the entire concept of inspiration, thanks to pervasive positivity memes on the internet.

Unless you count these

. But no, those images don't actually make me want to create my own; they just make me laugh.

I know lots of people have inspired me to do this or that thing, but just as I almost never do anything for just one reason, I also almost never do anything just because of one person. Like, long ago, when I decided to become an engineer, I couldn't point to any one engineer and say, "that person is the reason I became an engineer." No, it was a combination of things, like seeing locks on a canal and the Hoover Dam and the Brooklyn Bridge and any number of public works projects.

Which is not to say that everything was my idea. Far from it. Like I said, I'm not very creative. No one can do something without all the work that came before. Specifically, I'm thinking of Nikola Tesla, for example, or Isaac Newton, who supposedly said, "If I have seen further it is by standing on the shoulders of Giants." And then he went on to revolutionize everything.

When I was a kid, I think in elementary school, I have vague memories of an awards ceremony at the end of some school year. Like, they'd pick categories and hand out certificates. These days, from what I understand, such things aren't done as much because they leave out too many people, and I guess everyone gets participation trophies. This was also before the concept of "graduating" from elementary school. So anyway, a couple of things from that ceremony stuck in my mind, though I can't swear my memory of that time is all that accurate.

The first one was an award for "perfect attendance." When I was a kid, I'd catch a cold, or worse, at least once a year, necessitating that I stay home and be bored rather than go to school and be bored, and I remember thinking how unfair that particular award was. "Congratulations. You either never got sick, or you came to school anyway and infected the rest of us." At least I'm pretty sure I had the basic concept of germ theory figured out by then. Either way, I thought that was bogus.

But even more bogus, I thought, was someone who got the award for "most improved."

I can see your eyebrows furrowing from all the way over here. "How is that a bad thing?" you're asking.

Well, at least in my little-kid mind, I was going, "Huh. So if I'd started out getting bad grades, then gotten good grades at the end of the year, I could have gotten that award instead of "Biggest Pain in the Teacher's Ass" or whatever. See, I was savvy enough even then to never actually do my best work, and thus stand out as The Nerd. (It would be years before I learned to embrace my inner nerd, but by that time it was too late; I was already a committed slacker.) So I couldn't have gotten the "Best grades" award, but I could definitely have faked improvement over the course of a school year.

The actual award I got was so embarrassing that I don't even remember what it was; I only remember being terminally embarrassed by it.

The point to this rather lengthy digression from the subject is that the person who won that "most improved" award inspired me to always start out shitty so that people could praise me for having improved so much.

I don't even remember his or her name.

And if you don't think that's an important habit to get into, consider the well-known story of Einstein having failed mathematics as a kid. You might say that would make him the "most improved" thinker of all time.

Except that it turns out that the story, like Washington and the cherry tree, is completely fabricated. But it keeps getting repeated anyway, which just goes to show how that it's less important to simply be great, and more important to achieve greatness after having started well below average, so that people will think it could happen to them, too.

That's inspiring, isn't it?

10 Like • Comment • View 8 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.