Complex Numbers (Book)

Blog Calendar

◄ March ► 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 17 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 19 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.

March 27, 2020 at 12:11am

#979298

Lone

This is from three years ago, but it seems especially relevant now.

https://www.citylab.com/life/2017/04/how-to-break-the-dangerous-cycle-of-lonelin...

How to Break the Dangerous Cycle of Loneliness
Social isolation kills, and in the process it makes it harder to reach out to others. A psychologist explains how to stop the feedback loop.

I ventured out today, for the first time in a week and a half. Of course it was to buy beer. I encountered the brewmaster, who's a friend of sorts (always be friends with the brewmaster; that's your tip for today), and said that I've been pretending my self-isolation is a kind of virtue signaling instead of life as usual. I'll probably use that line, or something like it, in a Comedy newsletter.

Last year Surgeon General Vivek Murthy warned that Americans are “facing an epidemic of loneliness and social isolation.”

Funny, that word.

Loneliness is more dangerous than obesity, and it’s about as deadly as smoking. The threat is considered so serious that England has created an entire “Campaign to End Loneliness.”

So what if you're a fat smoker who is alone? I guess I'm fucked.

Also, if England wanted to end loneliness, maybe they shouldn't have self-isolated from the rest of Europe?

To learn more about this conundrum, and how to resolve it, I recently spoke with John Cacioppo, a psychologist at the University of Chicago who wrote a book on loneliness and has researched the phenomenon extensively.

Oh, hey, we haven't had a good book-shilling in here for hours.

First of all, let me qualify something. Living alone, being alone, and the size of your social network is only weakly related. Think about patients in hospitals: They aren’t alone, they have all the support they could ask for, but they tend to feel very lonely. There’s a difference between being alone and feeling alone.

I have a housemate, and we're friends, and I have other friends, including a bunch of people on this site. Physical distance isn't a barrier to friendship. Hard to drink with internet friends, but lately they've been doing workarounds for that. I'm kicking myself for not buying stock in Zoom before this whole mess started.

For instance, the internet has increased connectivity. But if you ever find yourself [looking at] your texts and emails at an event with your family, you may realize that those digital connections don’t mean that you feel more connected.

I grow weary of people ragging on internet-connected friendships. We've had this thing for more than a generation, now, and I was an early adopter specifically so that I could meet people - not get laid, but meet people - from other places. Family can be oppressive, and it's natural to want to escape their judgment in some cases.

And then the guy gets into evolutionary psychology, so I kinda skimmed that part. Pseudoscience.

Being with others doesn’t mean you’re going to feel connected, and being alone doesn’t mean you're going to feel lonely. It can, but usually we choose to be alone.

The majority of people are extroverts. I have to wonder if all this psych sorcery takes into account those of us who generally prefer to be alone.

Self-preservation depends more on your attention to your outcomes when you’re lonely than when you have lots of connections. [Sometimes] if you talk to a lonely person, they'll start talking to you and you can't get away. So, how do you share rather than just barrage? It’s about interactions, it’s about synergy, it's about mutuality.

Here's the thing about actual loneliness: it feeds on itself. I remember I was dating this chick back in college, and her roommates had put a thing on their bulletin board (we didn't have internet then) that went something like, "Wouldn't the world be a better place if depression and loneliness were attractive qualities?"

People sense loneliness and their instinct isn't to fix it, but to distance themselves from it, like it's some new virus coming around to infect them. This just isolates the lonely, depressed people more, and the cycle continues.

One of the biggest misunderstandings is what loneliness is. They equate it with being alone, and that leads to attempts to solve the problem that don’t solve the problem at all. And if you try enough times, you start to feel like, “Well, I’ll never be able to solve this, I’m just a worthless person.” And that's when you start getting social withdrawal.

Exactly. I need my alone time, but I also need some time with friends. Short periods, anyway.

Do volunteer service in something that you enjoy. I've developed the acronym EASE

And I stopped reading there (to be fair, it's near the end of the article). Whenever a shrink starts making up acronyms, they can be safely avoided. Oh, you're probably wondering what the One Weird Trick is to break the cycle. I'll save you the click: it's to go out and do stuff to help others. Thanks, that's helpful in these times. I'm going to crawl back into my shell now.

1 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.