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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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 5, 2020 at 12:01am

#997682

Ten Years After

What's the point of temptation if you have to resist it all the time? Tonight, I'm giving in to temptation with my response to this prompt.

PROMPT November 5th

Imagine the year is 2030. Write about what has happened in your life over the last decade in the past tense.

This past decade has been the longest century of my life.

It started, of course, with 2020. I remember the sayings well: "This year sucks." "Will this year ever be over?" "And we thought 2016 was bad." All posted on the internet, of course.

I miss the internet.

I miss computers and smartphones.

Hell, I miss electricity.

I tried to warn them, you know. Every time someone started talking about looking forward to 2021, I'd point out that things were only going to get worse. I didn't make a lot of friends, but that's the fun thing about being a pessimist: either you're wrong, in which case you feel good because something better happened; or you're right, in which case you get to be smug about being right.

Silly me. I thought I was preparing for the worst.

I never expected to actually survive.

The pandemic was bad enough. Then there were the riots. And the flooding. And the hypercanes. And the water shortages (which would have been amusingly ironic, considering the floods, but I stopped laughing after the first time I saw the tide of dead bodies washed up from a tsunami) that killed millions outright and displaced billions, triggering apocalyptic warfare.

I don't think anyone used nukes, but I can't be sure. Not around me, obviously. But the sunsets turned bright crimson for a while: dust kicked up by nuclear detonations? Or simple volcanic ash? All I know is the skies glared white in the day and the stars shone only dimly at night, and the hottest years on record got replaced with the coldest weather I'd ever encountered. I meandered south, hoping to be where it's warm, but the murder hornets and plague mosquitoes had the same idea, so I turned back to the frozen zones.

I always joked about how nuclear winter and a drastic decrease in population would be a surefire solution to global warming. Ha. Ha. Very funny. I was such a comedian.

I was able to scrounge, for a while. Fresh food became a distant memory. Plenty of cans, though. Dried beans and rice. After a few years, even in the cold, those staples started to go bad.

How did I manage to survive when so many fortunate others perished? I still don't know. Maybe I didn't. Maybe there is a hell after all, and I'm in it.

If not, then let it be known that my penultimate action in life was to leave this note where, maybe, one day, someone will find it.

I saw a bear out there. It looked hungry. Farewell.

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