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!

a day 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

a day 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.

June 3, 2019 at 12:05am

#960099

Dream Vacation

Our theme this week is Vacation!
Today's prompt is....

Tell us about your ideal vacation day!

One of the great things about being me is that pretty much every day is a vacation day.

Still, as you know by now, I do like to travel. But I also like to drink. These goals are, as I've noted before, contradictory.

So for now, let's assume that I'm not driving. First decision: Where to go? Well, that might depend on the time of year. While I prefer to spend as little time as possible outdoors, if I have to put up with cold weather for even a minute, it's less than ideal. Not a big fan of rain, either. That sets some boundary conditions.

Clearly, it has to be someplace where the alcohol flows like water. Scotland comes to mind - still planning to visit there next year - but it's not exactly tropical. So, while I'll do it, not ideal.

There doesn't have to be a lot to do. I'm not a fan of overdoing things on vacation. I fell into that trap a few times - fill the day with stuff to meet and people to do. Wait. Strike that. Reverse it. Anyway, at this point, the purpose of a vacation for me isn't to get away from all the hard work I'm not doing, but to simply be somewhere else, experience something that isn't the familiar surroundings.

So I know - let's go to Vegas again!

There, I can wake up whenever I want (always a key requirement on vacation), but that'll end up being earlier than I'm used to because it's a three-hour time difference. I can then saunter down to a bar and drink breakfast - possibly a bloody mary, or maybe a beer.

Then, gambling, because what the hell.

After that, I can get some lunch to drink, and maybe something to eat. Like tacos. Mmmm, tacos. That implies tequila. Or maybe a cerveza or dos. Or tres.

Then... more gambling! And a cigar or two. Maybe, if it's not cold, I'll venture into the not-so-great outdoors, seeking out microbreweries. All hail Uber. Or maybe another trip to Hoover Dam, the best tourist attraction a civil engineer could hope for.

For dinner, sushi. Vegas has some of the best sushi I've ever had (but I've never been to Japan). This means sake. Or maybe a good Japanese whiskey. Or, hell, both. Everyone has a superpower, and mine is being able to drink multiple styles of distilled and/or fermented beverages, in any order. This does, however, interfere with my gambling - playing blackjack while drunk is a Really Bad Idea. For the player. It's a great idea for the casino.

Then there's the Vegas nightlife. Oh, wait, I hate crowds. Better head back to the room and pass out. After all, wouldn't want to overdo it. Besides, gotta get up early tomorrow to drink breakfast.

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