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

September 15, 2009 at 6:59pm

#667879

Random Thoughts

A friend of mine just discovered the wonders of email. This means that she's currently forwarding every bit of glurge and misinformation on to all of her hapless friends.

I was just about to relegate her latest recirculated bit of "wisdom" to the compost pile when I accidentally looked at it.

And laughed.

So I looked at it some more.

This one's actually pretty good, so I'm sharing it. Just don't consider this permission to forward the latest sob story, questionable joke, or right-wing screed to my inbox.

Random thoughts from a friend of mine.

* I wish Google Maps had an "Avoid Ghetto" routing option.

* More often than not, when someone is telling me a story all I can think about is that I can't wait for them to finish so that I can tell my own story that's not only better, but also more directly involves me.

* Nothing sucks more than that moment during an argument when you realize you're wrong.

* I totally take back all those times I didn't want to nap when I was younger.

* The letters T and G are very close to each other on a keyboard. This recently became all too apparent to me and consequently I will never be ending a work email with the phrase "Regards" again..

* Do you remember when you were a kid, playing Nintendo and it wouldn't work? You take the cartridge out, blow in it and that would magically fix the problem. Every kid in America did that, but how did we all know how to fix the problem? There was no internet or message boards or FAQ's. We just figured it out. Today's kids are soft.

* There is a great need for sarcasm font.

* How the hell are you supposed to fold a fitted sheet?

* I would rather try to carry 10 plastic grocery bags in each hand than take 2 trips to bring my groceries in.

* I think part of a best friend's job should be to immediately clear your computer history if you die.

* Was learning cursive really necessary?

* I have a hard time deciphering the fine line between boredom and hunger.

* Whenever someone says "I'm not book smart, but I'm street smart", all I hear is "I'm not real smart, but I'm imaginary smart".

* How many times is it appropriate to say "What?" before you just nod and smile because you still didn't hear what they said?

* I love the sense of camaraderie when an entire line of cars teams up to prevent a jerk from cutting in at the front. Stay strong, brothers!

* While driving yesterday I saw a banana peel in the road and instinctively swerved to avoid it....thanks Mario Kart.

* Map Quest really needs to start their directions on #5. Pretty sure I know how to get out of my neighborhood.

* Obituaries would be a lot more interesting if they told you how the person died.

* I find it hard to believe there are actually people who get in the shower first and THEN turn on the water.

* Shirts get dirty. Underwear gets dirty. Pants? Pants never get dirty, and you can wear them forever.

* I can't remember the last time I wasn't at least kind of tired.

* Bad decisions make good stories

* Whenever I'm Facebook stalking someone and I find out that their profile is public I feel like a kid on Christmas morning who just got the Red Ryder BB gun that I always wanted. 546 pictures? Don't mind if I do!

* If Carmen San Diego and Waldo ever got together, their offspring would probably just be completely invisible.

* You never know when it will strike, but there comes a moment at work when you've made up your mind that you just aren't doing anything productive for the rest of the day.

* Can we all just agree to ignore whatever comes after DVDs? I don't want to have to restart my collection.

* There's no worse feeling than that millisecond you're sure you are going to die after leaning your chair back a little too far.

* I'm always slightly terrified when I exit out of Word and it asks me if I want to save any changes to my ten page research paper that I swear I did not make any changes to.

* "Do not machine wash or tumble dry" means I will never wash this ever.

* While watching the Olympics, I find myself cheering equally for China and USA . No, I am not of Chinese descent, but I am fairly certain that when Chinese athletes don't win, they are executed.

* I hate when I just miss a call by the last ring (Hello? Hello? Darnit!), but when I immediately call back, it rings nine times and goes to voicemail. What'd you do after I didn't answer? Drop the phone and run away?

* I hate leaving my house confident and looking good and then not seeing anyone of importance the entire day. What a waste.

* I like all of the music in my I Tunes, except when it's on shuffle, then I like about one in every fifteen songs.

* Why is a school zone 20 mph? That seems like the optimal cruising speed for pedophiles...

* As a driver I hate pedestrians, and as a pedestrian I hate drivers, but no matter what the mode of transportation, I always hate cyclists.

* Sometimes I'll look down at my watch 3 consecutive times and still not know what time it is.

* It should probably be called Unplanned Parenthood.

* I keep some people's phone numbers in my phone just so I know not to answer when they call.

* Even if I knew your social security number, I wouldn't know what do to with it.

* I wonder if cops ever get pissed off at the fact that everyone they drive behind obeys the speed limit.

* I think the freezer deserves a light as well.

* I disagree with Kay Jewelers. I would bet on any given Friday or Saturday night more kisses begin with liquor than with "Kay".

* The other night I ordered takeout, and when I looked in the bag, saw they had included four sets of plastic silverware. In other words, someone at the restaurant packed my order, took a second to think about it, and then estimate d that there must be at least four people eating to require such a large amount of food. Too bad I was eating by myself. There's nothing like being made to feel like a fat bastard before dinner.

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