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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Signature for those who have won a Quill Award at the 2020 Quill Awards

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10 Most Recent Blog Comments:

Write_Mikey_Write!

about 22 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 24 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 30, 2020 at 12:04am

#974524

Closing Time

PROMPT January 30

Congratulations on making it to the last day of the competition! What was your favorite prompt from the last month? Did you learn anything new about your fellow competitors? What was the most rewarding aspect of participating in the competition?

I had a better time with this than usual, this month. I don't know - maybe it was the musical selections I decided to do for a theme for the month. It wasn't always easy finding an appropriate song, in terms of lyrics, mood, and a title that would work as a blog entry (something I think I managed to do every day except for the first one). Music does tend to inspire me. Whatever the reason, I enjoyed almost every prompt. Especially amusing to me was the "naughty kid" prompt ("The Thin Ice"

) -- not only for making me remember the icy bay, but seeing the responses of others.

Which ties in with the "Did you learn anything new" question: Yes. Yes, I did.

Seriously, though, I've very much enjoyed the interaction with other bloggers - giving and receiving comments. Much thanks to all of you -- organizers, participants, everyone who stopped by, and, most especially, the lovely, talented, benevolent, fair, and incomparable judges.

I'm not going anywhere, though -- next month is February, home of the despised V-Day and my birthday, as well as crappy weather. The month has nothing else to recommend it, so I might as well keep writing in this thing.

To close out this month of musical theme tie-ins, here's a song that is not the song you think it is. But it's much better.

Yeah we're drinking and we're dancing
But there's nothing really happening
And the place is dead as heaven on a Saturday night
And my very close companion
Gets me fumbling gets me laughing
She's a hundred but she's wearing
Something tight
And I lift my glass to the awful truth
Which you can't reveal to the ears of youth
Except to say it isn't worth a dime
And the whole damn place goes crazy twice
And it's once for the devil and once for Christ
But the boss don't like these dizzy heights
We're busted in the blinding lights
Of closing time

6 Like • Comment • View 5 comments

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