Complex Numbers (Book)

Blog Calendar

◄ January ► 2008
S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

Signature for those who have won a Quill Award at the 2020 Quill Awards

Show Recent Comments

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

January 9, 2008 at 5:40pm

#560016

Tangerine

I picked up a couple of tangerines, today.

I've been eating those little bastards since I was a kid, but I never knew much about them. So I checked the internet, of course.

Skipping Wikipedia, I went to sources.

http://www.hort.purdue.edu/newcrop/morton/mandarin_orange.html

In 1965, the 'Dancy' tangerine was found to contain more of the decongestant synephrine than any other citrus fruit-97-152 mg/liter, plus 80 mg/100 g ascorbic acid.

Fascinating.

Yes, the article is about mandarin oranges. Turns out they're the same thing! Tangerines are varieties of mandarin orange.

http://mountainmandarins.com/documents/10Oct2005-MMGA.pdf

Leaving aside the questionable veracity of any document produced by someone named Fake, this is still pretty cool.

However, to quote one citrus expert, Lance Walheim, “The name tangerine has no botanical standing; rather it appears to have developed as a marketing term for bright colored (reddish-orange) varieties of common mandarin, such as Dancy”.

So... a tangerine isn't a tangerine. All my life, I'd been told it was a tangerine. My mother told me it was a tangerine. The store display today called them tangerines.

But wait! There's more!

Properly speaking, they are not mandarin oranges, but simply mandarins. However, since many Americans’ only acquaintance with mandarins is from a can labeled “mandarin oranges”, it may be helpful to call them mandarin oranges, even if it is not technically correct. Interestingly, DNA technology has revealed that the common or sweet orange is probably a hybrid of a pummelo, a large, thick-skinned citrus, and a mandarin. So, even your orange is part mandarin!

My orange is part mandarin?!

Well... at least I can find words that rhyme with "mandarin." "Hand 'em in." "Random win." That sort of thing. Not so, orange.

So I started to wonder: which came first, orange or the orange? In other words, was the fruit named after the color - or was the color named after the fruit?

http://m-w.com/dictionary/orange

Etymology: Middle English, from Anglo-French orrange, araunge, from Old Occitan auranja, from Arabic nāranj, from Persian nārang, from Sanskrit nāraṅga orange tree

Okay, so in Sanskrit, the orange tree was the root word for "orange." That tells me that, most likely, the color was named after the fruit. It still doesn't explain why the word has no rhymes, but I think I'll let that mystery sit for a while.

Just remember, though, next time you peel a juicy, succulent tangerine and pop its tart little sections into your mouth - you're actually eating a mandarin.

Comment • View 9 comments

© Copyright 2025 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.