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

January 17, 2021 at 12:01am

#1002263

Best To Not Think About It

PROMPT January 17th

What do you do to escape or distract yourself from negative thoughts and emotions? How do you take your mind off something you don’t want to think about?

Come on, now, I think everyone already knows my answer to this one.

But really, I have all kinds of avoidance behaviors, not just drinking myself blind. Usually if I immerse myself in a game (one that's a bit of a challenge, not, like, solitaire or whatever), it gets my mind to think about other stuff. Just going off to do something else sometimes breaks the circle of thought.

Thing is, I know that if something in my mind is nagging at me, I should confront it rather than avoid it.

I just don't wanna.

The best strategy, for me, one that is less directly self-confrontational but probably healthier than all of the above, is to start freewriting. Pretty soon my mind wanders and hey, maybe I even get a story out of the deal.

I haven't done that for a while, though -- so avoidance it is!

Mini-Contest Results!

Yeah, I didn't actually expect a lot of responses; it was a tough one. Sumojo

had the only relevant comment with:

I had been asked to be a bridesmaid for the fourth time in my life. The bride was my cousin and I was sure I was asked just to make up an even number.
We had never really liked each other, even as children but I agreed to participate once again. But what I really didn’t want was yet another horrendous bridesmaid’s dress which I’d never be able to wear again even if I altered it. The colours are always atrocious. Lilac or puce. I’m sure that brides select dresses for their bridesmaids to reflect on themselves. To show how beautiful they are and what plain friends she has.
I was bemoaning this fact to my mother, saying what terrible taste my cousin had and I wondered what her wedding gown would look like. “She’ll look like a meringue, I’ll bet.”
I saw my mother’s face go pale and I turned to see my cousin standing right behind me. Whoops!

And I just gotta say, that's a trope that when I see it in a movie or TV show, it never gets old: Character A is talking shit about Character B in front of people, and you see the people suddenly look uncomfortable and their gaze shifts, and Character A finishes with, "...and she's right behind me, isn't she?"

Way more embarrassing in person, I suspect. But hey, have a Merit Badge to take the edge off the shame, Sumojo.

7 Like • Comment • View 8 comments

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