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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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.

July 25, 2020 at 12:03am

#989070

Week

What day is it?

Merit Badge Mini-Contest below!

PROMPT July 25th

Reflect on your week. What was challenging? What did you do that made you feel successful? What made you smile?

Reflect on your week.

Time has lost all meaning.

What was challenging?

Keeping alcohol in stock. It keeps disappearing somehow. It's a mystery.

What did you do that made you feel successful?

Woke up in the morning. And again in the afternoon.

What made you smile?

Schadenfreude.

...okay, no, it's not all that bad. I'm well aware of what day of the week it is, and I know exactly why my booze keeps disappearing.

Sunday night, I managed to see the comet. It wasn't all that big a deal, but I had to try, because otherwise I'd never be able to look Phil Plait in the eye again. I wrote about the experience in this week's Comedy newsletter: "Comet Chameleon"

Speaking of the Comedy newsletter, I count getting it completed on Monday morning as a success, though no one saw it until Wednesday.

Getting back to the comet, though, I wasn't in any position to take pictures of it, but a whole lot of other people were. I think I posted a link to APOD here last week, but this site

has awesome photos also.

I have to admit, it's getting harder and harder to deal with being effectively unable to travel. Yes, yes, I know I could go do outdoors shit, but come ON, when do I do outdoors shit? No, the reason to travel, for me, is to drink at bars, stay in hotels, visit breweries, eat at restaurants, gamble in casinos (with money, not health), visit friends, go to Nerd Camp (cancelled this year), and generally be in places where other people are. In other words, I'm effectively unable to travel.

This especially sucks because it's right about now that I would have been leaving on another cross-country trip.

Yes, I know, other people have it way worse than I do. Fortunately, I'm not other people. If I can only kvetch if my situation is the worst possible situation, I'd never kvetch at all, and that's not fun.

But no, it's not "challenging." Just depression-inducing.

Fortunately, yesterday was National Tequila Day, and also fortunately, I had some in my stash.

Key word there is "had." Tenses are fun. In any event, tequila what made me smile most recently.

So, since I'm all down about the traveling thing, or rather the not-traveling thing, I think it's time for another Merit Badge Mini-Contest.

Write in the comments where we'd go if I met you on a trip. I don't know -- maybe thinking about it is a bad idea, but I won't know until I actually think about it. This can be somewhere unique to wherever you are, or some distant location; doesn't matter, since this is all hypothetical anyway (unless you don't want it to be, in which case hit me up when things settle down). Also, no need to limit this to things I talk about all the time; I'm up for new places and experiences. The answer I like best will earn the author a Merit Badge tomorrow.

As usual, deadline is midnight WDC time today (Saturday, July 25).

7 Like • Comment • View 11 comments

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