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 9 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 11 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.

June 20, 2021 at 12:01am

#1012194

Plans

We interrupt our regular programming to bring you this important message...

Do they still say stuff like that? I haven't watched network TV in years. Nay, decades. What with streaming and all, I get to set my own passive entertainment schedule and, bonus, avoid ads.

But no, really, today I'm not answering a prompt or discussing a link.

Yesterday, I went to see a friend. This is notable because it's the first time since the Before Times that I visited someone else's house. He and his wife have been my friends since, I don't remember, sometime in the 90s. It was his birthday celebration, and five of us just did normal stuff like taking a walk, playing a card game, having a barbecue, and talking about stuff.

You know, normal life things.

I'm fully aware that there's still a pandemic going on, which is why I decided not to go to Belgium this year, after all; the phased reopening of the EU is tricky to follow and I don't want to go at a time when stuff I want to do isn't available. So, hopefully, that'll happen next year.

Meanwhile, I've decided to do a road trip soon, which is mainly what I wanted to talk about here.

I've done an entry in this blog every day for just over 18 months now. Usually, I post something shortly after midnight WDC time. When I'm traveling, my schedule will be inconsistent -- I'm still going to shoot for every day, but it's unlikely that they'll all be at the time we've all grown used to here. But, honestly, I'm not going to stress about it; if I have to miss a day because there's other stuff going on, well, so be it.

18 months is, after all, a good run of posts.

So. Whenever I tell someone I'll be on a road trip, their first question is, understandably, "Where are you going?" While I get where the question is coming from, my road trips tend to be the living embodiment of "it's about the journey, not the destination." I might even say that there is no destination, only journey. That said, for this trip, I've picked out a few spots completely at random. It just so happens that at least two of those spots are relatively close to good friends from WDC, and I intend to visit them. I also intend to visit breweries and other points of interest.

I also take my time, often avoiding interstates. While US interstate highways a) are an everyday marvel of civil engineering (which was my professional life); b) represent a nice fast way to get from Point A to Point B; c) provide travel services such as food, gas, lodging, and toilets, most of which are helpfully signed; and d) were a triumph of infrastructure planning at the Federal level which couldn't be replicated today if we tried; they're also, with a few exceptions, exceedingly boring. I use 'em if I'm in a hurry, usually on the return trip when I'm starting to get tired of driving.

Consequently, if you happen to live near a place where I'm going to be passing through and want to grab a drink or whatever, I might be able to arrange that. But I don't precisely know where I'm going to be, except central Minnesota and, later, the Salt Lake City area. After that, probably I'll take a more southern route back east. If not, there's (hopefully) going to be a next time.

Make it worth my while (i.e. buy me a beer) and I might even be persuaded to take a detour.

My plan right now is to leave on Saturday. This means I'll be traveling over the July 4th weekend, which may suck, but the only other alternative would be to wait until after that holiday to start the trip, and I'd rather not wait that long.

So until then, blogging as normal. After that, well, we'll see.

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