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!

a day 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

a day 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.

June 5, 2019 at 12:07am

#960208

Go Away

Today's prompt has a bit of a twist....

1. Find 5 songs about vacation!
2. Plan a vacation using your favorite song

TWIST (this'll encourage you to read everyone else's posts...): no repeat songs!

Are you fucking kidding me right now?

Okay, fine, I'm going to claim the obvious one.

Have I ever mentioned I actually saw them live, once? I kind of always had a crush on the drummer. This shouldn't come as a surprise to anyone.

Let's go with this one for number 2 (so to speak)

https://www.youtube.com/watch?v=fJWmbLS2_ec

It's been half a century, and I still don't know what the fuck "the Kokomo" is. Other than a town in Indiana, which is hardly a vacation destination. Hell, even Springsteen mentions "the Kokomo" in one of his greatest songs, "4th of July, Asbury Park (Sandy)," which isn't a song about vacation, so I'm not going to include it here. Anyway, what in the ever-sucking SUCK is "the Kokomo?"

Number 3. I'm declaring that this counts. Margaritaville by Jimmy Buffett.

https://www.youtube.com/watch?v=ue2-ZVxpVjc

This counts too. Number 4. Sex Pistols. Because in the UK, "holiday" means "vacation."

https://www.youtube.com/watch?v=2Ah1JM9mf60

And for Number 5, I'm going to declare, by fiat if necessary, that this song is also about vacations.

For the record, this is one of the greatest songs of all time, as underrated and underplayed as it is.

Barkeep, another Mekong please
Yes, of course, you can keep the change
A new glass here for this new friend of mine
Forgive me, I forgot your name
Flip a coin, what shall we talk about?
Heads, I tell the truth, and tails, I lie
Well, I came all the way from Taipei today
Now Bangkok's pouring rain and I'm going blind again
And I haven't seen my girl for fifteen thousand miles

But is it true it's always happy hour here?
And, if it is, I'd like to stay a while
Well, as cliche as it may sound
I'd like to raise another round
And if your bottle's empty, help yourself to mine
Thank you for your time
And here's to life

Barkeep, we need to go around again
One for me and what's-his-name, my new best friend
So, deal me in and I'll pick my cards up off the floor
I'll see a lucky coin and raise a pack of lies
Smile to the girl at the door, another four dollar whore
But don't look her in the eyes, she'll break your heart
We came all the way from Taipei today
Still, Bangkok's pissin' rain and we're going blind again
And I haven't seen my girl in fifteen thousand miles

Well, is it true it's always happy hour here?
And if it is, I'd like to stay a while
Well, as cliche as it may sound
I'd like to raise another round
And if your bottle's empty, help yourself to mine
Thank you for your time
And here's to life

Well is it true it's always happy hour here?
And if it is, I'd like to stay a while
Well, as cliche as it may sound
I'd like to raise another round
And if your bottle's empty, help yourself to mine
Thank you for your time
Well, as cliche as it may sound
I'd like to raise another round
And if your bottle's empty, help yourself to mine
Thank you for your time
And here's to life
Here's to life
Here's to life
Here's to life
Again

So... "Plan a vacation using your favorite song."

No. That would put me in New Jersey, and I've already been there this year. Twice, technically. Er... actually, four times if you're really going to get technical about it. Went there, then NYC, then back to NJ, then to Boston, then drove through NJ twice on the way back home. It's not a vacation destination; it's a place where you drive through or end up.

Note: I've been drinking today. A lot. Probably more than I should have. Definitely more than I should have. This may have influenced the above entry.

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