Complex Numbers (Book)

Blog Calendar

◄ June ► 2021
S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 8 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 10 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.

June 17, 2021 at 12:04am

#1011997

Souperman

Entry #5 of 8 for "Journalistic Intentions"

[18+]

Don't cry because it's over, smile because the onion soup will taste great. -Max Kwoa

I suppose I could launch into a monologue that blasts the social expectation that men aren't supposed to cry. The pressure to conform to that stricture is still there, because we have yet to fully move beyond the whole patriarchal gender roles thing.

But you know, I'm not in the mood for social criticism right now. So instead I'll talk about how I finally learned to make French onion soup.

Cooking is another thing that men were traditionally not supposed to do. Well. Cooking at home, anyway, because that's not a paid job. It's always been quite alright for men to be restaurant cooks. This has to do with the perceived difference in value between "women's work" and "men's work," and...

Dammit. There I go again.

Anyway, fortunately, that particular taboo has been greatly eroded. Which is a good thing because if I were not allowed to cook, I'd be broke or dead from either eating out all the time or not eating at all. This is why single men don't live as long, on average.

Yeah, most of what I make is of the quick and easy variety. This is because I don't see much point in slaving over a hot stove for hours to make an elaborate meal for just me. Sometimes I'll make something and share it with my housemate, but mostly we do our own cooking.

But late last year, I got it in my head to make French onion soup because it was winter and I wanted some. Besides, everyone needed a pandemic hobby, right? It's a dish that takes a good bit of time, but there aren't that many ingredients and you can make a large batch to have leftovers.

It might surprise you that the principal ingredient in French onion soup is onions. Not French. And it takes beaucoup d'oignons. Er, I mean, a lot of onions. Oodles and oodles of them. And you gotta halve each one, and then slice each half into thin half-rings. While it's not as hazardous to the tear glands as completely chopping the annoying buggers, it still has the potential to aerosolize onion juice, which can lead to eye irritation.

There are a few ways around this hazard.

The first is to use white or red onions, not yellow onions. This, however, results in a less flavorful soup. Or, well, I think it does; I haven't tried it with anything but yellow, but in other recipes the other varieties just aren't as tangy.

The second is to have someone else cut the onions for you. This is out of the question for me, but it's always good to delegate. Just don't make your kids do it, or guaranteed you'll end up with bloody onions and them in the ER.

The third is to cut them under running water. This is a pain in the ass, and has the potential to make things more slippery -- see above about blood.

The fourth is cheating: wear goggles. That way the onion spray can't get to your eyeballs. Just remember not to touch your eyelids after you're done and have removed the goggles. Also remember to clean the goggles afterward.

Honestly? I don't do any of these things. Sometimes my eyes get a little irritated, yeah, but then I just wet a paper towel and wipe my eyelids with it.

Anyway, chopping all those damn onions is the most labor-intensive part of making French onion soup. The rest is mostly just caramelizing the onions, simmering them in broth and a few other secret ingredients, and, after topping each bowl with bread and cheese, making sure you don't broil the cheese so long it becomes charcoal. (I've always managed to get it right because I'm awesome).

I'm not going to provide the whole recipe. I found it online and so can you, and you might even find one that suits your taste better than the one I found. But I will note a few tips:

Experiment with the bread. I have had excellent results with challah, but that may be too chewy for some people. Traditionally, one uses baguette slices.

The optimum cheese combination is (in my own opinion of course) Gruyere mixed with a little bit of grated Parmesan. Sure, Parmesan isn't French, but who cares? Other than the French. Don't tell them, but all of their cuisine came from somewhere else too, just like almost everyone's.

Get a set of those purpose-made ceramic French onion soup bowls. It just doesn't work as well in a standard bowl. They're not all that expensive and you might even find some used.

In any case, the bread and cheese are not optional.

Wow. Normally after doing an entry like this I get hungry, but I don't have the three hours or so that it takes to do the recipe. Besides, I'm out of onions. So sad it makes me want to cry. But I won't, because I'm a guy.

3 Like • Comment • View 2 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.