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:

Write_Mikey_Write!

about 20 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 22 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

February 23, 2020 at 12:17am

#976124

Getting It Write

Every once in a while I get lazy. Okay, you got me - I'm always lazy. But today, very little commentary is needed.

https://www.theguardian.com/books/2017/may/13/so-you-want-to-be-a-writer-colum-m...

So you want to be a writer? Essential tips for aspiring novelists
How to write a killer opening line. Why Google is not research. When to rip it up and start again. Whatever you do, just write!

Since you're here reading this, I'm going to go ahead and assume that you're a writer. No one really knows what they're doing, and it's a lifelong learning process, so it doesn't hurt to go back to basics - if, indeed, these are basics.

There are no rules. Or if there are any rules, they are only there to be broken. Embrace these contradictions. You must be prepared to hold two or more opposing ideas in the palms of your hands at the same time.

That's actually good advice for a lot of things. While people who embrace contradictions are slammed as "hypocrites," the fact is we're all hypocrites. Being able to have two opposing viewpoints is a hallmark of humanity, not a condemnation of it.

Don’t write what you know, write towards what you want to know.

I always say "Don't write what you know; know what you write." (The above quote contains a comma splice, which breaks the rules, but hey, this author claims there are no rules. Fine.) Anyway, this amounts to the same thing.

Writing a character into being is like meeting someone you want to fall in love with.

Eh. Maybe. I'd add this to the section: just as you have to embrace your contradictory nature, characters have to have internal contradictions, too. Or they're boring. The article touches on this with "Complicate them. Conflict them."

Try not to use dialogue to convey information, or at least a slab of obvious information.

There is only one way to convey information: put it in the writing. One subset of this is to provide exposition. Another subset is to have characters explain things. Neither is always right. But there is such a thing as too much information.

In any case, as with all writing advice, take it or leave it. I just thought this particular article, ancient though it is (2017), was particularly thorough. Unlike this blog entry.

5 Like • Comment • View 1 comment

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