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

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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