Complex Numbers (Book)

Blog Calendar

◄ October ► 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	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:

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

October 25, 2023 at 9:51am

#1058039

Is There Anything It Can't Do?

More reasons why Prohibition was a bad idea, from Cracked:

4 Times People Had to Party to Survive

Admittedly, the headline turns out to be a bit misleading, but at least it's not from some other shameless clickbait site.

My first clue that the article wouldn't match the headline was the opening image which, if you don't feel like clicking, features a pool upon which floats a life saver ring, and inside the ring is nestled a can of Bud Light. So, water floating in water.

A deep love of partying is generally not the path to a longer life.

No, just a more fulfilling one.

Alcohol is a poison, but one that offers some good stories and a possibility to meet your future spouse at some karaoke bar.

Too much of anything is poison, and I still follow my ironclad rule, scraped from experience, to never pick up women in a bar. No matter how much I've indulged.

But what if drinking could save your life?

That would be known as a coincidence.

That said, there are a couple people throughout history who have somehow caught a lucky break off a usually harmful substance.

Okay, okay, we get it: you're badmouthing booze so you're not responsible if someone walks away from the article with "I should drink more." Enough with the moralizing.

4. Mark Wahlberg

Mark Wahlberg, or Marky Mark, was a bona fide rock star back in the day.

As I did not know, until reading this article, that these were the same dude, I reject the label "bona fide."

When an opportunity to go party at the Toronto Film Festival presented itself, he canceled his earlier plans, bailing on a flight he’d already booked for the next morning from Boston to L.A.

In short, the flight he missed was on the morning of 9/11/01. The article implies that Wahlberg wanting to party saved his life. A bit of a stretch. You know what would be really weird? If something like this didn't happen. There's probably at least one cancellation on every commercial flight; this one just happened to be someone moderately famous, and the flight he missed became more than moderately famous.

If he'd been a "bona fide rock star," what was he doing flying commercial?

3. Clifton Vial

Not even Warhol-famous, this time.

Essentially, dude drove around Nome (not exactly known for its tropical climate, lying as it does just a few miles south of the Arctic Circle) with nothing but a 12-pack of Coors Light.

He had decided to drive out on the roads to, and I am not joking here, see how bad the roads were. They were bad.

I've done that, admittedly. But I live in a well-populated area.

When his car got lodged in a snow bank where it, and he, remained for three days, he turned to the 12 Silver Bullets in his trunk for sustenance.

Might as well have just melted some of the snow...

Not a bad idea, given that any beer drinker can tell you that Coors Light is basically water anyways.

See?

2. Moe Berg

The amount of alcohol involved in this story isn’t as well documented... a dinner party where the guest of honor was famous physicist Werner Heisenberg...

One might say the amount of alcohol was... uncertain.

You could be forgiven for thinking that I linked and commented on this article because of the drinking bits. But you'd be wrong. No, I'm highlighting this article because it gave me an opportunity to make that pun.

The guest we’re talking about, however, was a man named Moe Berg, who was a major league baseball catcher, a polyglot and an American spy.

I bet he got all the chicks.

Seriously, though, read about this guy. As the article notes, he really did fucking rule.

In summary, Berg's mission was to essentially butter up Heisenberg to see how close the Germans were to making a working fission bomb. If the answer was "close," Berg (in his profession as spy, not catcher) was meant to assassinate the scientist.

I do have to wonder why he didn't just do the dirty deed anyway, considering that Heisenberg was, at the time, working for the Nazis, and Berg (despite having part of the physicist's name) was the son of Jewish Ukrainian immigrants to the US.

According to some interpretations of quantum theory (of which Heisenberg was a pioneer), there's another universe where he did just that. Probably one where no one at the dinner party had been drinking.

1. People with Antifreeze Poisoning

After that last one, this is a bit anticlimactic. Antifreezeactic? Whatever.

If someone finds themselves in a situation where they’ve ingested antifreeze or another substance containing ethylene glycol, a drink even more dangerous than rail tequila, alcohol can be used to save their life.

Now, look. I don't usually do disclaimers here. But don't take medical advice from a dick joke site. Or from me. Even the article is aware of this:

Of course, don’t read this and think if you accidentally chug some car juice, you can head for the liquor cabinet instead of the hospital and sleep it off. Anytime you drink poison, it’s best to have a doctor involved.

...unless that poison is ethanol, naturally.

6 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.