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 12 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 14 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.

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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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

May 21, 2020 at 12:04am

#984023

Useful

Today's discussion is about things that are easy to take for granted.

PROMPT May 21st

Not including your phone, computer, or other Googling device, write about the top five most useful items you own.

This is where I'd normally get into a philosophical discussion of the concept of "ownership," but I'll spare you this time. I'm in the middle of checking out a new superhero TV show, and I want to get back to it, so I'm going to keep this quick and simple. So without further ado, an off-the-top-of-my-head list of the five most useful things I own.

5. Refrigerator

Not only does this allow me to keep fresh food longer than would otherwise be possible, but its primary use is keeping beer and white wine chilled. Obviously, I don't chill reds. Except for Beaujolais Nouveau, but that comes out in November when I could just as easily keep it outside.

4. Toaster Oven

As a single person, I rarely have use for the big oven. The toaster oven sees some use almost every day, as does the microwave. Some things suck when they're microwaved, though, while the toaster oven gets it right every time except when I forget about it being on. But really, almost anything in the kitchen could be on this list, so, moving on...

3. Toilet

Indoor plumbing is one of the greatest inventions of humankind. I may be biased, being a civil engineer and all. Still, not having to venture out into the not-so-great outdoors just to take a shit, or deal with a disgusting chamber pot, is decadence incarnate. Also, as with the kitchen, everything in the bathroom could be on the list: sink, shower, closet, and my ever-dwindling supply of apparently irreplaceable toilet paper. I mean, come on, seriously -- it's been two months; why can I still not find Charmin anywhere? This is bullshit. Bullshit that I can't wipe up.

2. Bed

Chairs too, really -- without chairs, I wouldn't be able to use the items on the Forbidden List in the prompt quite as readily -- but it's much easier to sleep in a bed, and sleeping is really bloody important to me, especially after emptying the fridge of beverages. The bed is also adjustable, so I can read in it comfortably. The other traditional use for a bed is inapplicable to me, but even so, it's useful enough to make the second highest spot on the list.

1. House

The single most useful item on this list, because it contains all of the other items and then some. And yes, it's mine, not the bank's. It keeps me dry when it rains, cool when it's hot, warm when it's cold, and it offers a degree of security.

I suppose "car" could be on the list too, but I don't have a garage, so then I wouldn't have been able to say the house contains everything on the list. Besides, I could probably live, reluctantly, without a car (I have essentially been doing so for two months now), but being homeless would totally suck ass. Especially because there'd be no place to store the toilet paper.

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