Complex Numbers (Book)

Blog Calendar

◄ November ► 2023
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:

Write_Mikey_Write!

about an hour 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 3 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.

November 22, 2023 at 10:00am

#1059938

Drinksgiving

Today's entry isn't random, but inspired by "Invalid Item"

... today, the day before Thanksgiving in the US, and two days before Black Friday, we celebrate:

Blackout Wednesday

What's Blackout Wednesday? Well, you could just click on the link to find out. But for lazy folks:

Blackout Wednesday, sometimes referred to as Drinksgiving, takes place the night before Thanksgiving Day, and in some parts of the United States is one of the biggest drinking and party nights of the year. Many college students come back to their hometown for Thanksgiving, and go to bars the night before...

So, considering all the posts I do in here about fine fermented and/or distilled beverages, one might be forgiven for thinking that this is my kind of holiday.

It is not.

Not that I have any objections, mind. While I'm not above being a hypocrite, just like everyone else, I do make a conscious effort not to be. I remember college drinking culture (which probably means I didn't participate in it enough), and if I say I've never been blackout drunk, a condition I have labeled "danchu," which turned out to be a Mandarin Chinese word for "fade to black," as in a movie, I'd be lying.

I'm not above lying, either—I am, occasionally, a fiction writer—but I take drinking too seriously to deliberately make stuff up about it in nonfiction settings.

All of which is to say that I'm not judging anyone (unless they drive drunk, which I do get judgemental about), but Drinksgiving just isn't my thing.

There are several days on the official calendar—as opposed to the unofficial and mostly promotional calendar that I've linked to a few times this month, including today—that are devoted to drinking. These include such celebrations as St. Patrick's Day or Cinco de Mayo, as well as the more universal New Year's Eve.

I call them "amateur nights," and try to stay off the roads. Not because I'm drinking (necessarily), but because amateurs are.

And Drinksgiving is the ultimate Amateur Night; as the link demonstrates, it's all about college students (most of whom are still too young to drink legally in the US, but that's another issue and one I'm not getting into right now) coming home and drinking together. It's one thing to be a middle-aged occasional binge-drinker; it's quite another to have little to no experience with alcohol's effects.

Like I said, though, I was once one of those college students, so I understand, just like I understand why little kids play pretend or vroom model airplanes around.

Hell, I'm also a gamer, so I might even understand those things better.

It's widely known that with adulthood comes responsibility. While I, personally, avoid that as much as possible, college students are in that liminal space between other people being responsible for them, and them being responsible for themselves and others. Also, taste hasn't been altered by adulthood, yet, so there's less emphasis on what you're drinking than on simply getting danchu.

For instance, I had not yet developed my snobbery about drinking quality beverages; for my 21st birthday, I did 21 shots of Jose Cuervo, which is technically tequila in a way analogous to how Coors Light is technically beer—that is to say, it meets the arbitrary requirements, but still sucks.

As an aside, when I was in college, fermented beverages were legal for those 19 and older; they passed the law raising it to 21 on the day I turned 19 (and it didn't take effect until that July), so I was grandfathered in on beer and wine. Hence my 21st birthday hard liquor celebration.

I'm rambling, though, and I haven't even started drinking yet. My real point, here, is to dispel any misunderstandings about why I drink. Creating a really good beverage—that is, beer, wine, tequila, gin, or cocktail, e.g., is an art form, and I appreciate the art. Getting danchu is a bit like running a race through an art museum: you miss out on what is, to me, the best part of the experience, maybe glancing at the paintings and sculptures but without the time or inclination to really appreciate them, in favor of crossing that finish line.

I've noted before that many people, especially Americans (the only nationality I have great familiarity with, being one myself), don't have a middle ground. Either something is awesome, or it sucks. You either refrain from smoking weed, or you're a stoner. Either you're a teetotaler, or you're an alcoholic.

I reject that binary and live in the middle.

That is what I refer to as an alcohol-positive lifestyle: to acknowledge the downsides, while still enjoying the benefits. I guess that's part of the whole "responsibility" thing.

So, in brief, no, I won't be celebrating Drinksgiving or Blackout Wednesday or whatever you want to call it. But I'm also not going to rail against it. And I do have some fine craft beer to drink this afternoon... in moderation.

Not going to stop me from polishing off that entire bottle of Beaujolais Nouveau tomorrow, though. So in celebration of Thanksgiving, allow me to trot out my now-five-year-old Thanksgiving-themed poem:

Alcohol, Hookers, and Blow

(18+)
A Thanksgiving thanks giving
#2175291 by Robert Waltz

5 Like • Comment • View 1 comment

© 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.