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 the Bunny 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: one day closer to camping

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: one day closer to camping

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

Ѧͷͷΐ

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 Lucky

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

April 5, 2021 at 12:01am

#1007766

Procrasti-later

Here's another one for all my fellow procrastinators out there. I keep meaning to get a procrastinators' convention together, but can't ever seem to get around to it.

'Why Do I Spend Weeks Avoiding Tasks That Will Take Me 10 Minutes to Do?'
Procrastinating has less to do with time management and more to do with mood management.

The article is dated from mid-January and I'm just now posting it.

Sometimes we just can’t make ourselves do stuff! Last month, when I asked people to talk about times they’d opted to not do something that they could also simply… do… my mentions were flooded.

Example: taxes. Here in the US, the Federal income tax deadline is usually April 15, though it's been extended this year due to... you know. Individual states, the ones that have state taxes, have different deadlines. Either way, it needs to be done soon. My accountant has been bugging me, and I've collected most of what I need. The rest? Well. I'll get to it eventually.

I can't tell you how many times I've mentally prodded myself to Just Do The Thing and yet fail to do that very thing. Until it's the last minute. Or after. Blogging every day has helped a little bit with that, but the underlying problem (me) remains.

Whether it’s watching your plants wither for weeks before repotting them (total time to complete: six minutes) or waiting until you get pulled over to replace the registration sticker that’s been expired for a year (that was me, I did this), a lot of folks are procrastinating on alllll kinds of little things.

How about procrastinating on getting someone to edit your article?

Why, exactly? When it’s relatively simple to Do The Thing, and when the consequences of Not Doing The Thing can be serious or fairly unpleasant, why do so many of us look the other way?

Of course the article goes on to answer that question. It's a Vice article, not clickbait. Oh, wait...

“We get punished for being late in our culture,” Ferrari said. “We don’t get rewarded for being early.” And when you internalize the message that there’s no point in being early, you can apply that to any task that needs doing.

Well, that's just a matter of point of view, isn't it? If you're a procrastinator, things are often late and you suffer negative consequences. These consequences comprise your default. So anything better than the default is a reward, such as not suffering negative consequences. That's the same thing as a reward in my book.

“Procrastination is an avoidant way of coping,” Sirois said. “How do I manage uncomfortable feelings around that paperwork I have to do? I know, I’ll put the task aside and feel better about it. Ah, I feel better already. You just managed your mood by procrastinating.”

This makes sense. To go back to the taxes thing, I always end up owing money. I do not want to pay money. So I put it off. Which sometimes means I owe more money.

That fear of fucking up can keep you from starting in the first place—even if it’s a little thing like taking five seconds to write a text or answer an email. And on the other hand, if you do a good job... well, what if you can’t maintain it? What if you can’t do it as well the next time?

Which may explain at least one reason I haven't really pursued story publication.

Procrastination tends to be a solitary struggle, but literally everyone does it!

I know people who don't. Stop misusing "literally."

And if this behavior has become a regular occurrence—the kind of thing that’s paralyzing you in your personal and professional life or preventing you from reaching your goals—it might be time to talk to a professional. Chronic procrastination can be a symptom of anxiety disorders, depression, and ADHD; a mental health expert will be able to tell you more.

I've had a shrink's number pasted on my board since December. Have I called them yet? What do you think?

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