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 14, 2007 at 5:09pm

#488090

You heart WHAT??

Ah, Singles Awareness Day.

I was trying to figure out when the

symbol came into use, and ran into a lot of speculation and wishful historical thinking. The explanation I like best is that the flowers of a certain member of the parsley family resembled hearts, and this plant was used as a means of contraception in the ancient world. The plant, sadly, only grew in a limited area and became extinct - which I suppose says something deep and metaphorical about human nature, but it escapes me at the moment.

The

shape looks nothing like an actual heart, anyway. The human heart has long been known as the symbolic source of love, especially what we now know as "romantic" love. And I suppose that drawing the organ itself would be rather disgusting and, probably, turn thoughts away from amorousness. Unless your beloved is into that kind of thing.

So, okay, the symbol doesn't make a lot of sense either way. But what would you expect from something representative of that least rational of human interactions?

I'm not knocking it, you understand.

Back in the 80s there was this huge fad, perpetrated by the New York tourism people, to put bumperstickers on your car that read, "I (heart) [whatever]" - beginning with "I (heart) NY" and going downhill from there. "I (heart} Jesus;" "I (heart) my dog" and so on. It was slightly worse than the current "ribbon" trend, and not quite as bad as the "Baby on Board" signs from later in the same decade.

I found a big sheet of stickers that had line drawings of screws on them. You peeled them off and slapped them over the annoying hearts. "I (screw) NY;" "I (screw) my dog"... you get the idea.

Trends last until they're parodied. It did my

good to see, today, a black "ribbon" on the back of a truck that read, "Someone stole my awareness magnet!"

There is hope.

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