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:

Write_Mikey_Write!

about 2 hours 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

about 4 hours 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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

January 4, 2023 at 12:01am

#1042630

Mushroom Mushroom

I don't care what the source is (in this case, Field & Stream); I'm not going to swallow something I found in the (shudder) outdoors based on internet advice.

The 7 Safest Mushrooms to Forage and Eat
Perfect for novice foragers, these mushrooms are delicious, easy to find, and are not easily confused with toxic species

For reference, I've harped on mushrooms in here before: "Everyone Calls Me Mushroom Because I'm Such A Fun Guy"

is from about six months ago, links to an article by the same author in the same source—but from the other direction, talking about the bad fungi. Which, to me, is anything you don't find neatly packaged in the produce section of the supermarket.

As today's article is kind of the companion piece to that one, I figured I'd include it, too. For balance, if nothing else. I still have no intention of biting into a brown thing from the forest floor, but I guess some people like to live dangerously. Or, possibly, need to do something to survive; but that wouldn't be an issue if you didn't insist on going (shudder) outside.

There is some great eating out there in the fungal world, and some of the best-tasting mushrooms are also quite safe, with no or few poisonous look-alikes. But every mushroom article must carry a warning, so here goes:

Oddly, that warning isn't "don't go outside."

The good news is that there are local mushroom hunting groups that can educate you almost everywhere that mushrooms grow.

I have slightly more trust in the words of an expert with field experience, but, as the previous article noted, even experts can get sick or die from eating the wrong fungus.

The actual article has helpful photographs of the fungi in question.

1. Puffball Mushrooms

Kick or squeeze a mature puffball and clouds of dust-like spores will rise up.

And you want me to eat that?

2. Chanterelle Mushrooms

The only dangerous look-alike is the jack-o-lantern mushroom, which is bright orange, with true gills, while chanterelles have false gills.

Yeah, no.

3. Oyster Mushrooms

Another good mushroom for beginners, oysters are found on standing dead trees or logs.

Oh yeah, being named after sea snot, and growing on dead trees, really whets my appetite.

4. Chicken of the Woods

Finally, a wild thing that actually does taste like chicken.

You know what else tastes like chicken? Chicken.

5. Hen of the Woods

...are you fucking kidding me?

6. King Bolete

Very good or bad mushrooms tend to attract lots of nicknames.

My nickname for this one would have to be "forest penis."

7. Lion’s Mane

It’s in the tooth fungus family and doesn’t even look like a mushroom. It’s also called the pom-pom mushroom, because it looks like something a cheerleader would shake to rile up a team.

You know what it doesn't look like? Food.

Obviously, there's a lot more information in the article. And it's actually good and informative; I just have to rag on things to make myself feel superior. And don't get me wrong; I do like mushrooms, but like I said, I prefer the ones from the grocery store. Not that that's any guarantee of safety; hell, people have died from eating goddamn lettuce from the supermarket (it was contaminated with e. coli, as I recall). Life is full of risks, so why compound them by venturing outdoors?

5 Like • Comment • View 7 comments

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