Complex Numbers (Book)

Blog Calendar

◄ January ► 2020
S	M	T	W	T	F	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31
Archive				RSS

About This Author

Contact Me

Come closer.

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/

Signature for Honorable Mentions in 2018 Quill Awards

A signature for exclusive use of winners at the 2019 Quill Awards

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

Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 21 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 23 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 29, 2020 at 12:06am

#974473

After All

PROMPT January 29

Everyone did a great job with filling the war chest yesterday! There's so many great prompts and I'm sure Em will love every one of them.

Since today *is* War Chest Wednesday, I'm going to grab one.

What is your favorite virtue? Give a few examples like kindness, cleanliness, tact, truth, generosity. Is your favorite one you possess, or one you simply admire in other people? Do you have a strategy to develop it yourself?

Prompt is courtesy of Kåre เลียม Enga

Snark.

Wait, is that a virtue? No? Everyone hates it? Well, shit.

I'm glad Kåre เลียม Enga's other idea, the one involving a certain mouthless feline, didn't make it into the prompt. Still, I find the juxtaposition of "tact" and "truth" amusing, since those are sometimes incompatible.

Other examples of virtues? Well, I suppose there are two loosely defined kinds of virtues: directed toward the self, such as tenacity, self-control, or mental flexibility; and directed toward others, like charity, fairness, and loyalty. There might be a third kind, but it's intertwined with religion, and one does not need to be religion to be virtuous; sometimes, it seems, religion gets in the way.

But there's one virtue that, I think, influences many of these others, both inward and outward, and that is compassion. One can be compassionate to others, obviously; but it's also good to be compassionate to oneself. I know I'm harder on myself than I am on others, and I could stand to cut myself a little slack now and then.

Unfortunately, for myself, compassion isn't something that comes naturally. I have to think about it deliberately. I mean, my first reaction when someone's holding up a line at the grocery store, or cutting me off in traffic, or trying to sell me insurance, is usually annoyance. I have to reach for serenity, and I have to reach for compassion: knowing, logically, that everyone is the star of their own show, and they can each justify their own actions, and maybe they're just having a bad day. Maybe their dog just died, or their house has a leak, or they're worried about a friend.

And yet, compassion is the one thing I want to strive for. On a purely selfish level, it helps me as a writer to try to see others' points of view. But more importantly, I think that if I could crack the code of compassion, perhaps other people will appreciate it if they know someone cares about what they're going through, whatever that may be.

There was some discussion a while back about what people are "really" like. I believe that we have to practice being who we want to become. If something that you want to be isn't a part of your character, is it "fake" to try to practice that virtue until it becomes a part of you? I don't think so, myself; otherwise, how could any of us deliberately change? So, no, I'm not a compassionate person. But I'm working on it.

I'm not very good at it. It's not like I can learn it like I'm learning French, or like I learned how to do engineering. But I've seen peoples' actions that I have identified as "compassionate," and that's what I strive to emulate.

One such person that stands out for me is a lesser-known singer/songwriter named Dar Williams, who as far as I'm concerned is the Avatar of Compassion -- so it's her song I'm going to feature to tie in with this theme.

Go ahead push your luck
Find out how much love the world can hold
Once upon a time I had control and reined my soul in tight

Well the whole truth
Is like the story of a wave unfurled
But I held the evil of the world
So I stopped the tide froze it up from inside
And it felt like
A winter machine that you go through and then
You catch your breath and winter starts again
And everyone else is spring bound

And when I chose to live
There was no joy it's just a line I crossed
It wasn't worth the pain my death would cost
So I was not lost or found
And if I was to sleep

I knew my family had more truth to tell
And so I traveled down a whispering well
To know myself through them...

6 Like • Comment • View 5 comments

© Copyright 2024 Robert Waltz (UN: cathartes02 at Writing.Com). All rights reserved.
Robert Waltz has granted InkSpot.Com, its affiliates and its syndicates non-exclusive rights to display this work.