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:

Writer_Mike

about 11 hours ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

1 Like

QPdoll

a day ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

a day ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day 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

a day 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

Sep 21, 2024 at 7:34am
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

Sep 21, 2024 at 6:46am
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

Sep 21, 2024 at 6:16am
In response to "Paris, I Guess"

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

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
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.

February 10, 2023 at 12:01am

#1044536

Car Care

I don't really remember why, specifically, I saved this one. Perhaps I did so back when I didn't have a car to deal with.

How To Clean Car Seats
Let’s get that moldy cheeseburger cheese out from the seat cushion, okay?

Or you could, you know, not eat a cheeseburger in your car.

So you’ve hopped into your car only to find that something, somewhere, stinks to high heaven. After a little investigative nose work, you’ve discovered part of last week’s Taco Bell Nachos BellGrande fell between the seat and console when you hit a bump. Well, it seems like a great time to clean your car seats!

Or nachos. Or faux-nachos like the ones from Taco Hell.

Look, some things are okay to eat in a car. Anything that drips is not in that set. Crumbs are easier to remove than goo.

Cleaning your car’s interior, as well as regularly maintaining its luster, will not just make your everyday life that much better, it will also contribute to your car’s overall value when you decide to sell it—no used car buyer wants to find someone else’s toenails.

Toenails? Who in the name of all that's holy clips their toenails in the car? Come on.

And with a little elbow grease, a vacuum cleaner, and a bucket of soapy water, your car’s seats can go from trash-pit to palatial palace in just a few hours.

I got tired just reading that sentence. Also, "palatial palace?"

Estimated Time Needed: Two to four hours

Oh hell no.

We know a number of you likely also have children who are confined to child car seats.

Might want to take 'em out of there sometimes, especially when you're not driving them anywhere.

1. Remove the child's car seat from the car.

Okay, so, as you know, I've never had to deal with that sort of thing. And when I was a kid, we didn't have car seats; they just shut us in the trunk to roll around. But it seems to me that this step, alone, takes more than the four hours allotted to the entire car-cleaning marathon. And that's not counting the PhD in Car Seat Installation that you need to strap that sucker back in.

Reupholstering Your Car Seats

Listen, if you've had the car long enough to need the seats reupholstered, no one is going to give a shit if you clean the car, least of all you.

Source: my lived experience.

Getting Out Smoke Smell From Your Car Seats

Are you kidding? That smoke smell ensures that no one ever asks me for a ride anywhere.

It costs zero dollars if you clean your car seats and child seats yourself.

Well, that's a truckload of hokum right there. Way back at the beginning of the article, it listed a bunch of materials you'll need. None of those things are free. Not even the water. Hell, this whole "article" is an ad for car cleaning products.

If you have someone detail your car’s interior, then it could cost anywhere from $50 to a couple thousand dollars depending on who you enlist to do the job and the type of car you have.

And it's absolutely, completely worth every last dollar of that to keep me from having to clean something myself.

Life Hacks To Cleaning Your Car Seats

Important life hack: ignore any "life hacks" you come across on the internet.

Featured Car Seat Cleaning Products

"Zero dollars," my smelly-car-seat-sitting ass.

6 Like • Comment • View 2 comments

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