Complex Numbers (Book)

Blog Calendar

◄ November ► 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
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

November 27, 2022 at 12:01am

#1041062

Porsche Swing

Today's blast from the past is a short entry I wrote near the end of August, 2008: "I can't get no..."

I've been trying to put words to the malaise that seems to have overtaken my life. It's not that I'm not happy, or I'm severely lacking in anything (except maybe motivation).

I don't think I wallow in self-pity to that degree anymore. If I do, I don't write about it, because that leads to a) people shunning you even more; b) advice that doesn't work for me (as per some of the comments on that entry); or c) people being happy about it because at least they're not you.

Anyway, I did finally figure out what was bugging me, I think: work. The fact that I had to do it. It was interfering with my video game time.

What I want to focus on, though, is the first comment, from someone I sadly haven't seen in a while but used to comment here a lot:

It's "midlife crisis," buddy. I've experienced it and know men who experience it until either they self destruct or they do something to sate it.

Some people treat a midlife crisis, especially in dudes, as a joke. And to be fair, sometimes it really is funny, like when someone goes out and blows all their money and credit on a Porsche and a 21-year-old hooker (neither of which I've ever done). But that shit's real, and as much as society pushes men to squash their emotions, doing so is generally a Bad Idea.

That shit can ruin lives. I had an uncle who had an affair with a grad student, and ended up destroying his family. Fortunately, the kids reconciled with him before he croaked, and he expressed regret at his actions.

Anyway, I don't think that was one; I've always been prone to depressive episodes, regardless of age. And even if it was, I didn't have a family to ruin. Sure, I ended up getting divorced the following year, something which was in no way my fault [Narrator: It was a little bit his fault]. But having glanced at a few of the intervening blog entries, they weren't all gloom. Some of them were about my epidural for back pain, and anyone who's experienced chronic back pain can tell you it definitely affects one's mental health. And then there was a vacation, which apparently helped, too.

I did end up, over the following year, buying a new car, retiring, and traveling (in that general order). But the car was a Subaru, not a Porsche, and traveling is something I'd always wanted to do but was difficult while working full-time.

Whilst out and about yesterday in my new-to-me Subaru—after over a year without a car, I wanted to see what changes happened in my town, and besides, it was sunny and 70 damn degrees outside—I saw that we now have a Porsche dealership in my town.

I wasn't even the slightest bit tempted.

5 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.