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:

Annette in France

about 8 hours ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

about 12 hours ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

about 12 hours ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

about 17 hours ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

about 18 hours ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

about 19 hours ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

a day ago
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

Sum1's In Kalispell Montana

a day ago
In response to "Get Baked"

I have long advocated using only the oven for baked potatoes, and am guilty of punching holes in the tops of one. I don't use Aluminum Foil either. But my other half likes to nuke them first, or only nuke them. It's the speed thing for her. I prefer to take my time when I cook, and do things the way I do them, not her way. But, sometimes, ,ya gotta keep the peace in the house. She won't buy Russet potatoes, but those are the only ones to use for this. I may have to exert a little effort an buty Russets just for Baked Potatoes. She loves the English Chips (really enjoyed those in England when I was there, so maybe she'll like the link I sent her (from you!))

2 Like

Cubboo!

a day ago
In response to "Get Baked"

Yes! I discovered this a few years back (slitting the potato about 1/4 - 1/2" lengthwise, then one or two slits across the longer slit.) It came out wonderful! It seems like this was called an English jacket potato, or something like that.

2 Like

Annette in France

a day ago
In response to "Get Baked"

I'll try your oven baked potato in winter when it's sensible to run the oven for 90 minutes.

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.

8 Like • Comment • View 2 comments

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