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

August 8, 2008 at 3:23pm

#600878

080808

Just because it's too cool a date to pass up, here's a special 08/08/08 entry.

The number eight is binary 1000, octal 10, and in decimal, 2 raised to the power of 3, or 2*2*2. 8*8*8, taking this further, is 512 in decimal, or 1 000 000 000 binary.

August, of course, is named for Augustus Caesar, who might just be the greatest politician that ever lived. Yes, even greater than Barack Obama, and so much greater than Bush that they're not only not in the same ballpark, they're not even in the same sport.

I mention politics because, of course, 2008 is an election year; it's the 232nd year of American independence from silly British accents, except when we watch Bond movies or quote Monty Python. 232, of course, is 240 minus 8; and 240 hours makes 10 days, taking us back full circle.

Except that the whole 2008 thing is purely arbitrary; it measures passage of time from when someone 'way back when thought Jesus was born, and he turned out to be off by around four and a half years or so. Besides, more than half the world doesn't even consider Jesus' birth to be important enough to begin counting a calendar from, but they do it anyway, because when in Rome, y'know... don't piss off the Romans.

If it were up to me, I'd reset the calendar so that Day 0 of Year 0 took place on what would be 7/20/69 under that calendar. It was on that day that a human first set foot on a world other than our own, an accomplishment that should be self-evidently paradigm-shifting. Should be, but the number of people who think the space program is somehow a waste of resources - not to mention the number of people who think the whole thing was faked - continues to astound me. Well, I suppose that makes sense; I think religion is generally a waste of resources, and the whole Jesus' birth thing was faked, so I guess we're even.

So there you go - musings on a purely arbitrary date. Turn it on its side, though, and you have zero-infinity-zero-infinity-zero-infinity. Which is by itself pretty cool.

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