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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Show Recent Comments

10 Most Recent Blog Comments:

Turkey DrumStik

about an hour ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

a day ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

a day ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
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

February 20, 2019 at 1:42am

#952466

Germs! Germs! GERRRRRRRMS!

Everything in life is hazardous and it will make you sick!

https://lifehacker.com/clean-your-phone-right-now-1832426763

Flu viruses that are capable of infecting others, for instance, can last on hard surfaces for as long as 24 hours, according to one study. This means anyone who touches your phone in that time could be vulnerable.

Okay... this is not a bug; it's a feature. Anyone who touches my phone should become violently ill for a very long time. Don't touch my fucking phone.

“Foot and mouth disease is very rampant in small children at nursery school-age, too,” Papadakos added.

Isn't that... a cattle disease? Everything suddenly becomes more clear now.

If you have access to one, Papadakos recommends using a particularly high-tech cleaning method: a UV disinfection box you place your phone in, which eliminates germs and electronic devices in seconds. They’re available for purchase on Amazon and they’re becoming more common in public restrooms and universities, he said.

...this article paid for by the International Association of UV Disinfection Box Manufacturers.

If you’re looking for something a little less high-tech, Apple recommends using a lint-free cloth to clean your iPhone, the kind you receive with a pair of glasses.

Have you seen the price of glasses lately? I think I could buy 20 UV Boxes for the price of one lint-free cloth. And probably three or four iPhones on top of that.

So clean it as often as you would with your hands (and do it now, you’re doing us all a favor).

I really hate when I find articles like this. Yeah, okay, if you're sick, stay away from people and don't touch shit they're going to touch. But I got really tired of reading stuff like, "We examined [insert common object] and saw more germs than live on a toilet seat!" Well, yeah, because toilet seats get cleaned.

Look, unless someone in the vicinity has a c. diff. infection or something, germs are probably good for you. Your immune system needs exercise, too. Never, ever bring a black light to a hotel room (but do check for bedbugs). It's best to simply assume that everything is covered in a nice, healthy coating of immune-system-exercising germs.

Sometimes I wonder if 2/3 of us have stupid allergies because we're not exposing ourselves to enough bugs. But hell, I'm not a biologist, so I could be way off. I just usually follow the "if I can't see it, it doesn't exist" philosophy unless it's in a kitchen.

4 Like • Comment • View 6 comments

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