Complex Numbers (Book)

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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/

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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 7, 2020 at 12:03am

#995230

Urine Good Hands

Entry #3 for

Journalistic Intentions

(18+)
This is for the journal keeping types that come to PLAY! New round starts July 1!
#2213121 by Turkey DrumStik

Golden State Urology

My adolescent sense of humor has long provided me with the means to come up with exceptionally amusing names for different professionals and businesses. Inspired by the Three Stooges (The Holy Trinity of comedy) with their law firm of Dewey, Cheatham, and Howe, I came up with things like a dentist named Dr. Paine and an astronomy professor named Dr. Starr.

But, as with all things, the real world exceeded my meager imagination. For example, the spokesperson for the local power company, was, for a while, a guy named Phil Sparks.

You can't make this shit up. Well, you can, but you wouldn't be believed.

Or the state lottery PR manager who, at one time, was a woman named Paula Otto. (Get it? Poor Lotto? Well. I thought it was amusingly appropriate.)

So Golden State Urology can be considered, at best, a minor contender for Amusingly Appropriate Names. I mean, after all, you only need them if your pee *isn't* golden, right? Or if you're getting a vasectomy. Urologists do those, too. When I got mine, the urologist was kind of snippy.

It would be more appropriate to get a colonoscopy from a Dr. Brown which, given the frequency of that particular surname (behind only Smith and Jones in the US, last time I checked), it would be really strange if there were no proctologists with that name. But, as usual, I can't be arsed to look it up; besides, who wants that in your search history? Bad enough I've been going down a Google rabbit hole of British monarchs from the 1500s, so I'm probably on a List somewhere as "someone who likes beheadings."

One of these days I'm going to get in trouble for my internet searches, and I'll be presenting my WDC portfolio as evidence of my innocence. "I'm a comedy writer! Of course I searched for 'How to commit a funny murder!' Oh, and don't look at my porn."

But I digress. There are, of course, fewer appropriate surnames than there are unrelated ones, and I really should be saving this discussion for if one or more of the first four prompts come up. But the nature of pulling these up at random leads to the possibility that I won't get to talk about Dr. Croissant or Dr. Brain. If they do come up, well, I trust my own croissant-craving brain to come up with something else that's mildly amusing.

I'll close with two observations: Once, in my cross-country travels, I came across this place

, although a quick search tells me that the specific location of Bacon Printing Company that I found is no longer in business. That's sad. Point is, though, I was hoping that I found the place that prints BACON, but alas, it's just a regular printing company that uses paper.

As for my second closing observation, Robert Waltz can't dance.

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