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 an hour 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 3 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.

November 13, 2023 at 9:53am

#1059420

Secrets Revealed

Every once in a while, I run across something I didn't know about. Weird, huh? That I don't know something? Well, now I do.

A Secretive Food Culture Enters the Spotlight
Peranakan cuisine is a feast of complexity

I'd never heard of the culture, let alone the food. Obviously, I've never tried it. Honestly, Atlas Obscura, here, could have made this whole thing up, April Fools style, and the joke would have been lost on me. Naturally, I checked out the Wikipedia

page, with the understanding that those can be a spoof too. But nope... just an entire culture I'd never even heard of.

Jiu hoo char is a specialty of the Peranakans, a cultural group that stretches across Malaysia, Singapore, and Indonesia. While not Peranakan herself, my mother inherited her jiu hoo char recipe from my grandmother, who inherited it from my great-grandmother, who in turn learned it from her neighbor, herself a nyonya—a Malay and Indonesian honorific for married women of the Peranakan culture.

Somehow I doubt that these recipes translate well into Western standard cookbook recipes. But I don't know; maybe someone's tried.

As recently as a decade ago, there were fears that Peranakan cuisine might die out, due to the tradition of recipes passing only from mother to daughter.

Based on what I saw on the Wiki page, it's not just the cuisine but the culture itself that seems to be hovering on the edge of decline.

Just off New York City’s Union Square, Kebaya is the first restaurant in the city to focus on Peranakan food.

If there was going to be one anywhere in the US, I'd guess New York or Los Angeles. I visit New York fairly often; this is something I'd like to try.

Peranakan culture dates back to the 15th century. Derived from the Malay word anak, meaning child, Peranakan refers to the descendants of the Chinese seafaring traders who landed in Southeast Asia and married local Malay women. Today, pockets of Peranakan culture are scattered across Indonesia, Singapore, and the Malaysian states of Penang and Malacca.

I don't know enough to tell whether there's bigotry involved. We in the US don't have a monopoly on racism.

A key hallmark is how much care goes into each dish’s preparation. Take kuih pai tee, for example, a petite vegetable-and-spice filled pastry. Making the tart shells requires dipping a mold into a thin batter, and then dipping it into a hot vat of oil and removing it at just the right moment. Remove it too soon, and the shell crumples; leave it in too long, and it burns.

Yeah, that's a lot of finicky work.

Below are some of the unique building blocks that make up Peranakan food.

I won't go into this part. For once, though, I'm not put off by the graduate thesis food bloggers always write before getting to the practical part. I'm a little bit less ignorant than I was before I read the article, and that's a good thing.

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