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 11, 2020 at 12:22am

#983286

Road Trip

I'm not one to keep photos around. Everything else, sure, but some reminders I just don't want.

PROMPT May 11th

Look at a picture from your younger years. You don’t have to share the photo with us, but try to describe it in as much detail as possible. What led up to the photo being taken and what happened after?

But hey, what the hell, I do have a few pics of Young Me lying around, and some of them have already been uploaded right here. Because I can't be arsed to go find others, I'll use this one. And because it's already here, I'll go ahead and share it:

I'm the ugly bastard on the right, with the hair.

From the description within that item:

I spent most of the summer of '84 working for a surveyor - then left and did a road-trip to Florida with my friend Pat.

That was the summer that Born in the USA came out. I was about to enter my second year of college; Pat had just been graduated from high school.

We took a week to drive to Disney World, where two random girls came up to us as we hung out by a fountain and asked to take our picture. We still don't know why. Maybe she thought I was Mickey and Pat was Goofy.

This is not that picture, but it's from the same trip.

Some takeaways from this:

1. Working for a surveyor is hard physical labor. I've never been much of a bodybuilder, but damn, I was cut that summer.

2. Yes, I measure the epochs of my life in terms of Springsteen albums.

3. This represents the first and last time I went to Disney World.

4. Pat is still my friend. Honestly, I don't know how. We're very different, and besides, I met him because he was chasing the same chick I was. This was in middle school. Neither of us were successful. But he lives nearby, after having moved to several other states and back, and as luck would have it, he called me yesterday, just to catch up. We still road-trip on occasion, the last one being to Atlantic City.

5. Some people have looked at that photo and disagreed with the "ugly" description. But nothing has been able to change my self-perception, then or now. In fact, it didn't occur to me until 20 years later that there was some remote possibility that the girls who took the (other) picture did so because they thought we were cute. Or, at least, that Pat was.

6. Like I said, this is not the same picture. This was before digital cameras, so we never got copies. I have absolutely no memory of who shot the one above (by deduction, I think it was either my cousin in Tampa or a friend I had in Jacksonville), but it was probably taken with the Nikon my mom gave me for my high school graduation, the one that I used the entire time I did photography semi-professionally. I say this because otherwise, I don't think I would have it now.

7. Pretty sure it was my ex-wife who scanned this one in. Like I said, I don't care much for pictures, certainly not enough to bother to scan them.

I'd made decent money that summer, with the surveyor, and the plan was always to do the road trip. We took our time heading south, stopping at campgrounds and seeing sights. The trip took place in August, which is probably the worst time to go to Florida, and the one thing I remember more than anything else is how freaking hot it was -- and also the summer thunderstorms in the Wang, every day at 3 or 4 o'clock. Those at least cooled things off for a bit, but did nothing to help the oppressive humidity.

That summer birthed my lifelong aversion to being outdoors, camping, and crowds, but it also made me realize that I really like road-tripping. It's just that my definition of "roughing it" now is staying in a three-star hotel.

Being young and idiotic, we both ran out of money while in Florida. This led to a mad dash back up the coast with our last $20, which back then stretched a pretty long way with food and gas. That of course resulted in me being broke once I got back to college -- an entire summer job's earnings, gone just like that -- but I was used to being broke at college. It wasn't until much later that I actually figured out how to be good with money.

All this remembering has given me a massive headache. Beer should cure that. I'll get right on it. And meanwhile, I'll just be wishing I could take another road trip. Preferably one that doesn't involve camping. Maybe someday...

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