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 6 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 8 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.

January 26, 2022 at 12:09am

#1025394

Everything Louder Than Everything Else

First of all, there might be erratic post timing from me over the weekend. I'm going beer tasting out of town. (Still don't have a car; someone else is driving.)

And now for a "JAFBG"

[XGC] prompt...

Have you ever run into the "Is this all there is to life?" existential crisis? How do you get past it?

No.

It's not like I've never asked myself that question; it's just that it never sank to the level of "existential crisis."

The root cause of existential crises, as I see it anyway, is that we're fooled into believing that life has a meaning, or a purpose.

It does not.

Believing that it does necessarily results in thinking about what that might be. Some people might find their own meaning or purpose, and they're content to live in accordance with it. That's fine, too. All I'm saying is that the initial assumption is faulty. You can build a house on a strong foundation, but if the underlying soil is unstable, it doesn't matter how solid the house is or how strong the foundation is; it will crack, tilt, sink, or get washed away in the next flood.

Once you realize that, ultimately, nothing has a meaning save that which we project upon it, you can just live life.

I'm sure a bunch of people would question the invalidity of that assumption.

"Isn't the purpose of life to reproduce?" That's a big part of the definition of life, but it's not a "purpose." Besides, we can choose not to do so, as I have, and still lead a satisfying life. Sometimes more satisfying, because there's less drama and disappointment involved. (Let's table for now the question of whether we actually choose anything.)

"But what about all the bearded philosopher types who claim to have found the meaning?" What about them? None of them stand up to objective scrutiny, as is obvious because the beards each have their own, often mutually exclusive, take on it.

"Forty-two!" Oh, give it a rest already.

I guess the philosopher who sums it up best for me is Jim Steinman, who wrote the following immortal lines for Meat Loaf to belt out:

Who am I? Why am I here?
Forget the questions, someone get me another beer
What's the meaning of life? What's the meaning of it all?
You gotta learn to dance before you learn to crawl
You gotta learn to dance before you learn to crawl

If you want my views of history, then there's something you should know
The three men I admire most are Curly, Larry, and Moe
Don't worry about the future, sooner or later it's the past
If they say the thrill is gone then it's time to take it back
If the thrill is gone then it's time to take it back

4 Like • Comment • View 7 comments

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