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:

🌝 HuntersMoon

Sep 20, 2025 at 12:12am
In response to "Numbers End"

Boy, am I behind thee times. I thought you just put this on hiatus. Of course, in March I wasn't a complete devotee of your brilliance yet.

I'm more than happy with Carrion Luggage, however.

1 Like

Elisa, Snowman Stik

May 1, 2025 at 7:09pm
In response to "Shhhhhhh"

Anytime I hear/read about the Quiet Zone, I am always reminded of this video.

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:16pm
In response to "Penultimatum"

As my Grandmother used to say, "Everything changes except that which stays the same." I never did understand why she said it, but it sounds good.

1 Like

TJ says, "keep on keeping on!"

Mar 12, 2025 at 8:13pm
In response to "Numbers End"

Looking forward to the new book and hoping you don't encounter a meteor.

1 Like

Lazy Writer est 4/24/2008

Mar 12, 2025 at 4:19pm
In response to "Numbers End"

Sorry this one is closing..I will look for the new one tomorrow! Looking forward to it.

2 Like

Aiva Raine

Mar 12, 2025 at 3:45pm
In response to "Numbers End"

Thanks for a great 3000 entries.

Looking forward to the new blog, whatever it might be.

2 Like

Wordsmitty ✍️

Mar 12, 2025 at 1:36pm
In response to "Numbers End"

OK. What have you done with the real Robert Waltz?

Also, for the scientist engineer in me, have you actually tried to make entry 3001 and been rejected. Until there's proof, it's not real.

Thank you for your indulgence and sharing of wisdom.

R.I.P. "Complex Numbers"

3 Like

Anni Pon

Mar 12, 2025 at 11:20am
In response to "Numbers End"

Sorry that this one is coming to an end, but I'm excited to see what you have in store for the new one!

2 Like

Wordsmitty ✍️

Mar 11, 2025 at 1:42pm
In response to "Penultimatum"

It's been an enlightening run. We wish you well in your next adventure.

It will be interesting to see if after the next entry that WDC actually does stop you from adding another.

We're all waiting on pens and pencils for the unveiling of the new blog and to discover what it will be called.

1 Like

BIG BAD WOLF is Merry

Mar 11, 2025 at 10:46am
In response to "Penultimatum"

I'm reminded of this scene from The Princess Bride.

(Vizzini has just cut the rope The Dread Pirate Roberts is climbing up)
Vizzini: HE DIDN'T FALL? INCONCEIVABLE.
Inigo Montoya: You keep using that word. I do not think it means what you think it means.

3 Like

February 2, 2009 at 5:55pm

#633524

Vacation spots

I figure, why not expand on last entry's "25 things," one at a time? This is, after all, the month containing my birthday, so a bit of introspection is, perhaps, forgivable.

1. My favorite vacation spot is Belize. My second favorite is New York City. Go figure that.

This is actually fairly simplistic and possibly misleading. I've been to Belize exactly once and, while we enjoyed it a great deal, we don't have plans to go back just yet.

Though there are islands for sale just off the coast for a remarkably reasonable sum, considering. About what you'd pay for a upper-middle-class house in my town.

If I were upper-middle-class I might even consider it.

Anyway, like I said, I've been to Belize once, but there are two places we go almost every year: New York City (NYC) and North Carolina's Outer Banks (OBX). So really, you could consider OBX my favorite vacation spot, and NYC my favorite place to visit.

The distinction is important. There's virtually no reason to visit OBX except to vacation, while the reasons for visiting NYC are manifold, especially since my wife and I both have relatives there. You may remember I went there - alone - last month. Well, I'm going again - this time with my wife - this month.

The occasion (apart from my birthday) is the first American concert in 15 years for Leonard Cohen.

You might not have heard of Leonard Cohen, but I can almost guarantee that you've heard at least one of his songs.

http://en.wikipedia.org/wiki/Leonard_cohen

I had a bitch of a time getting tickets. Apparently they were sold out prior to the official tickets-on-sale date. Unable to score tickets from the respectable, conventional and price-gouging Ticketmaster site, I turned to the disreputable, unconventional, and oh-my-god-you-want-HOW-much? reseller market.

I won't disclose what I paid for tickets. I will say that I've never paid that much for Bruce tickets. In my defense, Bruce plays huge stadiums and a whole lot more often. There are opportunities of scale. Yes, Bruce is a lot more popular, but Cohen has a devoted core following of fanatics. Wait, so does Bruce. Anyway, the point is, I scored tickets.

Having secured entrance to the exclusive concert, I set about finding transport and lodging. Transportation was a no-brainer; from where I live, it's more expensive to fly than to take the train; the train is a lot more comfortable, though slightly longer from door to door. And no one strip-searches me before getting on the train. So - train it is. Got a decent price for round-trip tickets, and no 3am departure times, either.

I decided to get creative with lodging. Like I said, my wife and I both have family there, but we wanted to be answerable for our time to no one but ourselves, so we wanted to get a hotel room.

Hotel rooms in NYC can be outrageous. More expensive, even, than scalped Leonard Cohen tickets. But this is New York City in February. February is the month people escape NYC, not enter it. So I decided to look for a bargain.

Before I looked for bargains, though, I remembered something about Nikola Tesla; how he spent the last 10 years of his life in a hotel in Manhattan called the New Yorker. Wouldn't it be cool, geek that I am, to stay in the same hotel? What are the odds that one of those early-20th hotels would still be standing, and still functioning as a hotel?

About the same, I guess, as the odds of me getting Leonard Cohen tickets:

http://newyorkerhotel.com/index.html

More, they're running a winter special, and it's costing us less than $150 a night to stay there.

Less than $150 a night, in the middle of midtown New York City, less than a block from the train station.

The optimist in me cheered.

The pessimist figures there's going to be one HELL of a blizzard that week.

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