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:

Turkey DrumStik

about 3 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!

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

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').

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

January 15, 2019 at 1:00am

#949681

It's a Trappist!

Where in the world would you like to visit the most? Assume you are not worried about money in any way. While you're traveling, give me a status update on January so far. Smooth sailing, or turbulence?

It's a close call between Scotland and Belgium.

The reasons are similar: Belgium makes some of my favorite beer, but there are some Belgian beers that don't make it out of Europe, and I want to drink them. As for Scotland, well...

Ideally, I'll visit both places before I visit the Great Pub in the Sky, but if I had to choose... well, I've actually been to Scotland, if only for a couple of hours whilst touring the UK, so I'd pick Belgium.

I have a friend who also loves scotch, and we have tentative plans to visit the island of Islay,

home of - depending on your feelings about scotch - either the sweetest nectar of the gods to ever grace our benighted world, or the most disgusting waste of good barley to ever besmirch the noble name of Scotland.

Naturally, I'm in the former camp. But it's okay if you don't like Islay malts; there's a limited supply, and the more people dislike them, the more there is for me to drink. Heavily peated whisky is probably an acquired taste. It is certainly an expensive one.

As for Belgium, well, Belgian beer is also not for everybody. The particular strains of yeast involved in the brewing process are quite distinctive, and impart a flavor that their fans call sweet, and their detractors liken to old gym socks. As with scotch, well... that means more for me. Traditionally, Belgian beers were brewed in monasteries. Many still are. The Trappist ales and abbey styles remain among my favorite beers.

So many drinks. So little time.

For the past month or so, I've been working on losing weight. This involves the usual weight-loss regimen: eating less delicious crap and more disgusting vegetables, and exercising. It also means not drinking as much as I'd like to. I want to emphasize once again that this was NOT a New Year's resolution, because I don't do New Year's resolutions. I started back in December, after coming back from a trip to Nevada and California that involved a lot of fine dining and even finer drinking.

If I can make it another three days, it will have been four weeks. If so, I'll celebrate with a glass of wine and start working on the next four weeks. But I do take some small satisfaction in knowing that, thus far, I've been successful in avoiding temptation.

That won't last, of course. I will fail, as I always do. But for now, I'll take the win.

5 Like • Comment • View 8 comments

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