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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 17 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 19 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.

March 26, 2020 at 2:31am

#979216

A Unique Perspective

So today I'm going to discuss actual writing again.

https://ideas.ted.com/helpful-advice-for-aspiring-writers-of-all-ages/

Helpful advice for aspiring writers of all ages

I find when something is targeted at "all ages," it often ends up being infantile. Lowest common denominator and all that. Let's see here...

Being a writer is all about expressing your unique perspective with feeling and originality, not about having a huge vocabulary or getting published, says author Jacqueline Woodson.

Let's get this out of the way first: You don't have a unique perspective.

Neither do I.

In the time BI (Before Internet), you only had to be unique among a small group in order to stand out. Two things have happened in the last 50 years to change the landscape entirely: the population of the planet quadrupled, and we all started talking to each other. Now, in order to the the "best," you're competing with 7 billion other people. It can't be done. Not only that, but even if you're not concerned about "best," with that many people, statistically, someone else shares your opinions and talents.

And second, there's no such thing as "originality," unless you want to make up your own language.

“Write something good, and feel good about writing it.”

in response to the question “What’s the goal of writing when you’re 15?”

I know when I was 15, I felt good about my writing. Boy, am I embarrassed. Fortunately, none of that tripe survived.

“Writing is about narrative language and creative language and being able to get a point across in a way that is not ordinary. More than having a large vocabulary, one needs a large vision and be able to see the world in a different way than other people see it.”

Despite what I said above, I think this is decent advice as far as it goes -- though it doesn't express how someone without this ability for perspective might gain it.

If it’s possible, set limits on the initial feedback you receive

“When I first write something, I show it to three people I trust. I tell them: ‘Tell me every single thing you love about it.’

Doesn't really work on this site, unless you have a group set up for just that.

Being a writer means being a re-writer

Yeah, that's where I always stumble.

“Whenever kids start asking me about their stuff getting published, I’m like, ‘That’s not what you should worry about. You should worry about writing the best piece that you possibly can.’ Writing is such a process.

And again, not bad advice. But the promise of the headline - "for all ages" - fails, as usual.

2 Like • Comment • View 10 comments

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