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

November 13, 2020 at 12:01am

#998246

We Just Disagree

One great thing about living a drama-free life is there's little opportunity for disagreement.

PROMPT November 13th

Write about a disagreement you had with someone. What happened? Was the conflict resolved?

And yet, I have cats. Consequently, disagreements happen on a regular basis.

Cat: I hunger. Provide the customary nourishment, please.

Me: I just fed you.

Cat: Your memory is faulty. Behold, the receptacle is void of sustenance.

Me: That's because you ate it all.

Cat: ...I hunger.

And so it's resolved by me feeding the cat.

Similarly, when it's time to go to sleep.

Me: Cat, you're in my spot.

Cat: You must be mistaken. I have claimed this location by virtue of prior habitation.

Me: That is exactly where I need to be in order to sleep. You're a cat. You can literally sleep anywhere.

Cat: I must reiterate My claim.

Me: *picks up cat and gently deposits her on floor*

Cat: You are cruel! I have never been so mistreated in My life.

Resolution: Cat ends up sleeping on top of me so that technically, we're in the same spot.

Or, like, I'm trying to write a blog entry.

Cat: This keyboard, its temperature is pleasing unto Me.

Me: Cat, I'm trying to type here.

Resolution: I finish the blog entry later.

Now, I also live with a human, but fortunately, we rarely disagree and never seriously. This is probably because our relationship is what you'd call platonic: few expectations involved. I'm sure I get on her nerves sometimes, but as it's my house, I can live with that.

When I was married, though, my wife and I got into minor disagreements quite often (though rarely major ones, the exception being when she decided I had too much stuff). But that's too far removed in time for me to remember the details of any of them. Having a lousy memory has its advantages sometimes.

I'm tempted to joke, "We compromised and did what she wanted," but that would be unfair to both of us. I'm pretty sure I got my way at least once. Maybe even twice.

I have a friend I've known since middle school, and we see each other sometimes. We disagree on most things political, but it's not like there are any stakes involved. He presents his point of view and I present mine, and we're still friends.

In short, while I have strong opinions about some things, I don't let that get in the way of getting along with people.

Usually.

12 Like • Comment • View 8 comments

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