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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Turkey DrumStik

about 9 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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').

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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

October 9, 2018 at 12:29am

#942999

Who

So... I've seen every episode of Doctor Who.

I mean, as much as I could, anyway. A great deal of the early material has been lost, probably forever. But a few years ago, before the 50th anniversary, I went and found every episode, including the lost ones that were re-created from stills and audio tracks (and a few that were redone in animation), and watched them. Old Who, new Who, all of them. Didn't get to the 90s movie until later, but eventually watched it (almost wish I hadn't).

Well, I haven't gotten around to watching the recreated 4th Doctor episode Shada yet, but as it never aired when it was made, it doesn't really count. Still, I'm going to watch it at some point, because Tom Baker will always be "my" Doctor.

There's been a lot of hype about the most recent incarnation, which premiered Sunday. New Doctor, new companions, new composer, new showrunner... lots of new stuff there. In a way, that's good - it's accessible to viewers who haven't gotten into it before and don't want all that baggage. I was, I suppose, cautiously optimistic (because far be it from me to be completely optimistic about anything).

Don't be scared. All of this is new to you, and new can be scary.

Well, I'm here to tell you that the 13th Doctor *is* The Doctor. Thoroughly, completely, without a doubt. She nailed it. The other actors nailed it. The writers nailed it. The composer... well, jury's still out on that, but no complaints.

We're all capable of the most incredible change. We can evolve while still staying true to who we are. We can honor who we've been and choose who we want to be next. Now's your chance. How about it?

I would say that if science fiction / fantasy / horror / adventure aren't your thing, you probably still won't like it. But if they are, and you haven't seen Doctor Who yet, and have been intimidated by the weight of 55 years of history attached to it... now's your chance.

Of course, now that I've posted this, the rest of the season might very well suck. Many episodes do. You can't be a show like that and not sometimes have your experiments fail. But that doesn't take away from this first episode, which, as I said... nailed it.

4 Like • Comment • View 4 comments

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