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 28, 2020 at 12:03am

#974398

No Surrender

PROMPT January 28

Let's fill Emily's war-chest of ideas!

What's a topic you've always thought would be a great 30dbc discussion, but has never come up in the prompts? Why do you think it would stimulate discussion?

I guess I've been doing these challenges on and off for over a year, now. I can't say I've "always thought" a particular prompt would make a good discussion -- I save my prompt energy for my weekly contributions to "Invalid Item"

. I'm content to go with the flow and see where someone else's prompts take me. Also, my memory is crap so there's no guarantee that anything I come up with hasn't already been done, even if it was in a month in which I participated.

So I gave it some thought, and thought some more, and then worked backwards. I figured since I've been doing the musical thematic tie-ins all month, I'd just pick one of my favorite songs and go from there. Any prompt I propose here is going to come from either humor or pathos -- or perhaps both at the same time, as the line between them is sometimes blurry, and sometimes nonexistent. So this one is brought to you by Bruce Springsteen.

We've all heard the pep talk: "Don't give up! Never quit!" Like many pep talks, this can be harmful in the long run. There are times when the best thing you can do is to give up, abandon your dream, change course, retreat... surrender. Have you done this? Or have you actively resisted it? Either way, what was the result? Any regrets?

Why would this stimulate discussion? Well, I think it's likely we've all been there. When you face a challenge, sometimes you win, and sometimes you lose; sometimes you press on, and sometimes you just let it go. It's relatable and, I believe, could help people examine their own habits and motivations, and isn't that what self-reflection is all about?

I could write about this from both sides - fulfilling a goal, and on the other hand abandoning a different one. Neither one made me particularly happy or sad in the long run, so my assertion is that, for me, it doesn't matter -- what matters is having goals in the first place.

If you want specifics, though, you'll have to wait until it becomes an official prompt -- and that's assuming that I'm participating at the time. And that I remember what I was thinking of, besides the music.

Well, we busted out of class
Had to get away from those fools
We learned more from a three-minute record, baby
Than we ever learned in school
Tonight I hear the neighborhood drummer sound
I can feel my heart begin to pound
You say you're tired and you just want to close your eyes
And follow your dreams down

Well, we made a promise we swore we'd always remember
No retreat, baby, no surrender
Like soldiers in the winter's night
With a vow to defend
No retreat, baby, no surrender

8 Like • Comment • View 3 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.