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.

April 15, 2019 at 1:17am

#956598

Vacation

Apparently, I can either play video games, or I can blog every day.

That's okay. I need a break every now and then.

One thing I have been sticking to is my eating less and exercising plan - surprising, because I was sure I would have failed by now. But I keep seeing positive results (that is, negative results in terms of weight), so somehow, I've managed.

That will all change come Thursday.

As this is my blog, I suppose I could provide a bit of background. Feel free to skip it if you don't give a shit.

I was raised in a Jewish family. My mom's side is from New York City. She had two sisters and a brother. One aunt, A, stayed in NYC and never married or had kids. The other aunt, E, moved to Indiana (of all places) and raised two kids there. Now, the religion thing is relevant to the story because A was very religious and we'd often have Passover seders at her place. E, in contrast, has been an atheist since before I was born. (Yes, I take more after E, but I was always closer to A - go figure.) So - bear with me, here - one of E's kids, who is a bit older than I am, moved to Manhattan from Indiana and married a born-again Christian. Later, E ended up moving back to NYC as well.

If you managed to untangle the above genealogy, you'll realize that A was both my aunt and my cousin's aunt, so we had that in common. And being that they were in the same city (albeit a good hour away; NYC is big), they saw each other more than I saw either of them. But some years, we still got together for Passover seders - though none of the rest of us were religious in any meaningful way, I did it for my heritage and my family.

Aunt A died a few years back, right when NYC was buried under three feet of snow. That put the "fun" in funeral, let me tell you. Anyway, ever since then, my cousin's wife - the Christian one - has taken it upon herself to organize a family seder every year, to honor her husband's side of the family, mostly Aunt A. This is actually a bigger deal than it may seem, because doing it right is work, and since Passover usually starts around the same time as Easter (a holiday she observes), things get busy for her. So I respect her for that.

All of which is to explain why I'm going away for a few days. I mean, I'll still be "here," as in I'm bringing my laptop with me, but this is the first real trip I've had since I started the whole weight-loss thing.

So I'll probably be bad. I might even be very, very bad. At a minimum, as you might know, the Passover seder includes drinking four glasses of wine. But since it's been so long since I've gone anywhere - Vegas back in December - I'm planning on taking the opportunity to drive to the vicinity of NYC early, find a brewery to sample, and then, after I see the family, I'm hoping to find even more breweries in the general area to visit. Make it a week - Thursday through Wednesday.

Bastards are probably all closed on Easter, though - but I'm sure I'll find something to do. I'm just hoping that the siren call of the Atlantic City casinos doesn't overwhelm my desire to sample new and interesting beers. We'll see.

When I return - there's a deadline for that as I already have a ticket to Avengers:Endgame on that Thursday - I can back off on the overindulgence again. Consider this a vacation. And maybe I'll pour one out for my Aunt A.

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