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.

August 10, 2022 at 12:02am

#1036332

Loose Morels

I talked about poisonous mushrooms a few weeks ago, here: "Everyone Calls Me Mushroom Because I'm Such A Fun Guy"

. Today's article, from Atlas Obscura, is about a non-poisonous one. Well, sort of. Well, not really.

The Mysterious Mushroom That Only Grows in Burn Scars
To find fire morels, forage after wildfires.

You mean... go... (shudder) outside?

Also known as burn morels, these fungi grow exclusively and prolifically in the ashen moonscapes of recently burned forests.

I have to wonder how many cases of arson were people wanting rare shrooms.

They’re toxic raw but have a subtle, umami flavor when cooked.

And that right there is enough to make them a great big nope from me. If you have to cook something to make it non-poisonous—especially if you happen to be camping in the middle of a burn scar—it's not worth it. I mean, what if you don't cook it enough?

Fire morels, which Steinruck says have a mild smokiness to them...

If they didn't, I'd be concerned. More concerned.

The trek is challenging, from the terrain and from the fire. Spivack warned me that “after a fire, it’s even harder to get a toehold after everything’s burned. The slippery wet ash seems like an ice rink under the duff, without tree roots holding the soil in place. Burned-out stump holes and root channels can lead to a nasty fall if you’re not paying attention to where you step.”

And you thought a trip to the grocery store was loaded with (morel) hazards.

Apart from the stupid amount of time and work required to forage for these fungi, there are some interesting bits.

“There’s such big questions on how [fungal roots] can persist for so long before a fire,” says Ron Hamill, a mycologist who has been researching burn-related fungi for the last 15 years and is currently working on a book.

Please, please let the book be titled something like "Loose Morels." I'll also accept "Morel Support."

One reason that morels remain so mysterious is that they are nearly impossible to distinguish from each other. “We were really limited [in research] before by our ability to just identify fungi,” says Sydney Glassman, a professor at the University of California, Riverside. But technologies such as DNA testing and stable isotope testing are changing that. Her lab uses molecular analysis and bioinformatics to identify pyrophilous, or “fire-loving,” fungi.

And another reason not to bother: the possibility of misidentification. I know I don't carry a DNA kit around with me when I go (shudder) outside.

All of that notwithstanding, I still think it's cool as hell that even after a raging inferno, life, uh, finds a way.

Mostly, though, I had to make the pun in the entry title.

4 Like • Comment • View 4 comments

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