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 3, 2010 at 4:55pm

#686318

This Song's Just Six Words Long

But what inspires today's entry isn't great Weird Al parodies but an article about six-word stories.

http://www.npr.org/templates/story/story.php?storyId=123289019&sc=fb&cc=fp

Can You Tell Your Life Story In Exactly Six Words?

...Smith's six-word memoir? "Now I obsessively count the words." And Fershleiser's: "Bookstore to book tour in seconds."

Wait... "Fershlieser?" Who's Fershlieser? Snoop Dogg's ghostwriter?

Anyway... six word biography, huh? Seems like a tall order unless you're, like, four: "Potty training finally worked - whoo hoo!"

So here's one I've done off the top of my head:

"Six isn't nearly enough for me."

Which, of course, could be taken the wrong way. Which is the way I like it

Comment • View 6 comments

February 2, 2010 at 9:03pm

#686222

And if your head explodes with dark forbodings too

Okay, yes, shitty of me to end the last entry with a cliffhanger like that.

Thing is, I don't want to go into too many details. It's not me; it's my wife, and while most of my readers don't know either of us, I always walk the line between oversharing and not sharing at all. And sometimes I lie or exaggerate just to throw people off - I am, after all, a fiction writer.

But my wife really did have brain surgery yesterday. The timing was unexpected - the surgery was planned, though not scheduled.

She's had epilepsy for many years, and her seizures - which aren't what you think of when you think of seizures, but are something far less obvious - had been mostly controlled through medication. Not completely, though, and often, they've had to change the medication.

The doctors - and I'm not exaggerating when I use the phrase "a brilliant team of neurologists and neurosurgeons;" keep in mind this is the same place that worked on Superman - had been talking about finding and excising the source of the seizures for some time, but they've never been able to localize it.

Until now.

Mid-month, she had surgery to implant electrodes on her brain. It took them a week to figure out that the electrodes were not exactly in the right place to find what they needed. So then they went in and placed more electrodes - a grid of them - against the surface of her brain. The purpose of all these electrodes is diagnostic; they use them to pinpoint the source of the seizures.

Now, here's where I have some bad news for cyberpunk fans: the human brain really, really hates having stuff in it other than thoughts, memories, and images of Hugh Laurie. Anything physical, like, say, electronics, and it starts to attack the interloping object(s) like a mother bear defending her cubs' honor.

This particular grid of electrodes was adjacent to the part of the brain that controls things like reading, talking, and being able to watch House. So those functions began to deteriorate, and she wasn't having the seizure that they needed to locate the source. They were getting ready to pull out the electrodes before they caused anything more than temporary dysfunction, when they got lucky and she had what they euphemistically call an "event." Only no one brings potluck.

That was when they decided that as long as they a) knew where they needed to cut and b) had to go back in to remove the electrodes anyway, they might as well take out the offending bit of gray matter.

With her unable to articulate her opinion on the subject, it fell to me to consent to the procedure. I told them I had half a mind to go ahead with it, but if they fucked up, they'd get a piece of my mind. No, actually, I decided that neurosurgeons have probably heard those puns more often than I've told the Scotsman joke, so I only thought about saying that.

So anyway, they did it. It remains to be seen how well it worked, but they had confidence in the procedure, saying it was low risk (any surgery carries a risk, but we take risks when we drive to work in the morning) and had a high probability for success. "Success" being defined as "fewer to no seizures."

There was a time today when I was worried, but she's better now. Couple more days in the hospital, they say, to recover more. Three surgeries in a month's time is more than most of us have to endure.

Really, in retrospect, the decision was a no-brainer.

Comment • View 9 comments

February 1, 2010 at 1:00pm

#686020

Is This Thing On?

Okay, yes, it's been nearly a month since I've posted here. Sorry about that. I had it in my head that if I didn't blog, I'd write more stuff that I could - you know - publish. Well, that didn't work out so well.

Anyway, on to the actual reason I'm posting now:

Long-time readers will know that I'm a huge fan of the now-classic "Calvin and Hobbes" comic. I spent all my winter-solstice-holiday money a few years back on the hardcover collected complete edition, and the next three months reading them and laughing my ass off.

Hell, C&H even inspired a story of mine:

Home Again

[13+]
A middle-aged man rediscovers his childhood.
by Robert Waltz

It's well-known that Bill Watterson, the mastermind behind the greatest comic of all time (except for maybe Pogo), is a rather private person, content to collect his royalties in seclusion. I imagine him sitting atop a pile of gold coins, cackling madly (because that's what *I* would do). But now, on the 15-year anniversary of the (timely and appropriate) end of C&H, he poked his head out of his treasure lair for an interview.

http://www.cleveland.com/living/index.ssf/2010/02/bill_watterson_creator_of_belo...

This part is my favorite:

How soon after the U.S. Postal Service issues the Calvin stamp will you send a letter with one on the envelope?

Immediately. I'm going to get in my horse and buggy and snail-mail a check for my newspaper subscription.

Classic. Absolutely classic.

Oh yeah, and my wife is going to have brain surgery this afternoon.

Comment • View 2 comments

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