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

June 15, 2024 at 9:11am

#1072676

My Way or the High Way

From The Guardian, a fairly recent article featured in their "The High Road" section, by that prolific author named Anonymous...

Smoking weed every day makes me less presentable and less productive. I love it

Hey, now, I'm less presentable and less productive, and I don't smoke weed. Well, not often, anyway.

When the pandemic came, I moved back in with my parents in Los Angeles. It was extremely boring.

So are those sentences.

One night we had completely run out of things to do so they decided to go to a local dispensary and pick up.

I don't understand "completely run out of things to do." There's always something to do. Like, maybe, weed.

Smoking with them in the pandemic turned me into a habitual user.

That's right, your parents made you do it.

Now every morning I wake up, I get a fresh pot of coffee brewing and I finish the joint I was smoking last night before bed, which is sitting on my bedside table. When I’ve finished that, I roll another and continue.

Congratulations! You just discovered "Wake and Bake." Literally no one has ever done that before!

Last week my therapist asked me what it’s like being this kind of low-level stoned all day...

Well, there's an obvious way for the therapist to find out firsthand.

Am I addicted to it? Probably, but it works for me and I’m functional.

The first step is to admit you have a problem. The second is to lean into it and decide you like the problem.

Maybe it makes me less motivated, but I don’t really want to be more motivated. I consider wanting to be more productive very lame, like you’ve been cucked by the patriarchy and capitalism.

And that, folks, is a major reason the patriarchy and capitalism have spent the last century or so demonizing cannabis.

I smoke behind the wheel, using my car’s coin tray as an ashtray.

Fuck me, I'm old enough to remember when we used car ashtrays as coin trays.

Personally, I think weed just doesn’t do what alcohol does to you, especially in slow LA traffic. Obviously it is dangerous, but the only road accidents I’ve been in were from before I smoked weed – like driving past an ex-boyfriend’s place and being so in my head that I drove straight into a stationary car.

Okay, look, we all know I like to drink booze. And I generally have no problem with cannabis and would like to see it widely legalized. But driving while impaired is a line I don't cross. Now, sure, you can probably argue, though I don't have the data to back it up, that driving stoned isn't as bad as driving drunk or texting while driving. The problem isn't that you could hurt yourself, but that it's dangerous to other people.

I hate sounding all mud-sticky about this sort of thing, but that's where the author kinda loses my sympathy. "The only road accidents I've been in were from before I smoked weed" could very well be a matter of luck and survivorship bias, like if I said it's perfectly safe to ride in the bed of a pickup truck because I did that when I was a kid and I'm fine.

Last week, my dad called me while I was driving to work and smoking a joint. I made the mistake of picking up and he told me off for driving while I’m high.

Yeah, gonna side with Dad here.

Obviously this means my car smells powerfully of weed, which is not really a problem until I have to use valet parking, but the valets usually find it funny and ask me if they can hotbox it.

Clearly, the author's been lucky enough to never be stopped by cops, either. That's the #1 excuse they give to establish probable cause for a vehicle search, which gives them the opportunity to plant evidence for things that are more clearly illegal, like unregistered guns or meth: "A strong odor of marijuana was noted." (Police reports love to use passive voice.) In the author's defense, though, cops have been known to claim that when they just feel like harassing someone.

I once got kicked out of the parking lot at work for smoking weed and listening to fast jazz too loudly...

Ugh. Jazz? Pfeh. I guess the old scare tactics were right about the connection between weed and jazz. Me, I'd prefer the traditional musical accompaniment: Pink Floyd.

Which, honestly, I prefer to enjoy sober. But to each their own... except, in my opinion, when it comes to driving.

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