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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🌝 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.

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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

July 7, 2007 at 8:13pm

#519717

Ad Astra

We are all in the gutter, but some of us are looking at the stars.
-Oscar Wilde

I've been trying all day to come up with the right words, but without much luck.

I want to say something to commemorate the life and work of Robert A. Heinlein, born 100 years ago today, but I find that everything I think of has either been said before, or doesn't do the subject justice, or both.

Thing is, if you've read Heinlein, you already have your opinion - and if you haven't, nothing I say is going to make a difference.

It's not that I agree with everything he wrote, or aspire to be just like him, or consider him to be the "best" writer - there have certainly been better, both within science fiction and without. It's more that what he wrote influenced my thinking more than any other author.

He had a way of taking your assumptions, your dearly-held basic ideas about the way the world and society work, and stripping them down to the practical. Taboos are exposed as mere hoary tradition, and traditions venerated only to the point where they continue to make sense to an evolving society. As any good science fiction writer will, he came up with alternative societies - with alternative taboos, neither better nor worse than his own society's, just different.

Take a scientist's scalpel to all of your basic assumptions, be it the nature of family, the inviolability of the laws of physics, the definition of "love," everything your priests and shamans have told you, even what you think you know about yourself. Pare it back like a corn on your big toe. It can be painful, and there's no anesthetic, but when you're done there can be this immense sense of relief and accomplishment. For a while it's like there's something missing, but you quickly get used to it.

I think the best I can do now is let the Master speak for himself.

Always listen to experts. They'll tell you what can't be done and why. Then do it.

Writing is not necessarily something to be ashamed of, but do it in private and wash your hands afterwards.

There is no such thing as luck. There is only adequate or inadequate preparation to cope with a statistical universe.

Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something.

Thou art God, and I am God and all that groks is God.

History does not record anywhere at any time a religion that has any rational basis. Religion is a crutch for people not strong enough to stand up to the unknown without help. But, like dandruff, most people do have a religion and spend time and money on it and seem to derive considerable pleasure from fiddling with it.

One man's "magic" is another man's engineering. "Supernatural" is a null word.

The truth of a proposition has nothing to do with its credibility. And vice versa.

What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what "the stars fortell", avoid opinion, care not what the neighbors think, never mind the unguessable "verdict of history" - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your single clue. Get the facts!

One man's theology is another man's belly laugh.

Everything in excess! To enjoy the flavor of life, take big bites. Moderation is for monks.

Theology is never any help; it is searching in a dark cellar at midnight for a black cat that isn't there. Theologians can persuade themselves of anything.

How you behave toward cats here below determines your status in Heaven.

Never attempt to teach a pig to sing; it wastes your time and annoys the pig.

The United States has become a place where entertainers and professional athletes are mistaken for people of importance.

Nobody has ever seen an electron. Nor a thought. You can't see a thought, you can't measure, weigh, nor taste it- but thoughts are the most real things in the Galaxy.

Love is the condition in which the happiness of another person is essential to your own.... Jealousy is a disease, love is a healthy condition. The immature mind often mistakes one for the other, or assumes that the greater the love the greater the jealousy.

The more you love, the more you can love, and the more intensely you love. Nor is there any limit on how many you can love. If a person had time enough, he could love all of that majority who are decent and just.

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