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

November 28, 2007 at 12:30pm

#552121

Aren't you a little short for a stormtrooper?

These days, it's hard to find just one, solitary thing that you can point to and say, "There it is. There is the Sign that the end is near; that we've reached the Cosmic Cul-de-sac and some asshole's U-Haul is blocking the turnaround." But here's a candidate:

http://www.flickr.com/photos/redandjonny/

Maybe Problematic Content

needs to meet these folks.

There were comments about the religious slant of one of my blog links yesterday. Now, everyone knows by now that I'm not Christian; I make no secret of it. And yet, stuff like that doesn't bother me much.

Stuff like THIS religious psycho freak nut - this bothers me:

http://news.yahoo.com/s/ap/20071128/ap_on_re_us/papa_pilgrim;_ylt=A0WTUdJ7CU1HfP...

A man who called himself "Papa Pilgrim" and took his family far from civilization to raise them according to his interpretation of the Bible was sentenced to 14 years in prison for sexually assaulting a daughter.

...

Hale insisted that he had a perfect spiritual understanding, his wife, Kurina Rose Hale, testified Monday.

Now, after reading the article, think about it for a moment - consider possible reactions and results had the guy professed to be ANY other religion. As it is, most of us read that article and think, "That guy was a psycho, and it's no reflection on Christianity in general." But what if he'd been Muslim? Hindu? Wiccan? I suspect there'd be a lot of "Oh, it was because he was <whatever>."

I don't doubt that there's a bias concerning our American majority religious inclination, and that bias can work both ways. I've known Christians who automatically trust someone because he or she professes to be Christian. I've known other people who automatically distrust for the same reason - and honestly, I've fallen into that trap, thanks to some bad experiences.

But then I realized:

People are people. Some of them are okay (naturally, all my readers fall into this category). Most are idiots. Some few are sociopathic, psychotic, dangerous. Most of each of those groups are religious in some way; some are not. But professed religious leaning is no indicator of what a person is like; it is, at best, a rough guide to a person's beliefs, and beliefs may or may not manifest themselves in actions. The converse is true as well, though we, as humans, tend to ascribe to a group the characteristics of the representatives of that group (which is why a lot of Christians distance themselves from Pat Robertson, and why many Pagans distance themselves from Silver Ravenwolf - they're embarrassed by those representatives of their religions).

Bottom line for me is, judge by the deed, not by the creed.

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