Complex Numbers (Book)

Blog Calendar

◄ January ► 2019
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:

Turkey DrumStik

about 3 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

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

Nov 14, 2024 at 12:10pm
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

January 28, 2019 at 12:54am

#950612

Schadenfreude

Write about something happy in your life! What’s happened recently that made you smile? What’s the last thing you laughed at?

Life is darkness bleak, a swirling void of colorless numbness spiraling into the eternal event horizon of...

Okay, okay, enough with the angsta rap.

Still, you may have noticed that I'm not one to focus on happiness.

It seems important to many people, though. I don't know if it's just an American thing, since it's right there in our Declaration of Independence along with a lot of rants about King George III. That line - the "pursuit of happiness" - makes it seem like happiness is something to work toward, instead of what it is, which is a state of mind that emerges from other things.

What other things? Well, it depends on the individual, I suppose; that's the whole point. I'm anticipating a lot of "my kids of course!" answers, and if that works for you, great. For me, every time I see some whiny brat in public - provided that I have the option of walking away - I grin like a little bitch because I don't have to deal with that crap.

So, there's something that makes me happy.

Other peoples' misfortune makes me euphoric, as well. Not if it's undeserved, though. I'm never happy to hear that someone's been dealt a crappy hand through no fault of their own. But when I see some skaterat rack himself on a metal handrail, well, endorphins course right through my body and my sense of righteous retribution is satisfied.

There was a story a few days ago about some so-called "Instagram Influencer" (I looked it up and was grumpy for several hours straight because something like that exists) who was trying to take a selfie at the rim of the Grand Canyon and... well, you can guess what happened.

As one wag noted in a comment about that selfie that had me laughing for about a week, "Started out in portrait, ended up in landscape."

Lots of things make me laugh, but that one stands out in recent memory.

Yeah, I realize this makes me a terrible person, but I figured out a long time ago that I'm less angry when I embrace that than when I try to gin up sympathy in myself where none actually exists. But like I said, it has to be an example of karmic justice; someone falling off a cliff when they were just trying to enjoy a nice hike in the outdoors - even though that's something I wouldn't do, myself - is sad. Someone falling off a cliff while being a thrill-seeking attention whore? You're damn right I'm going to laugh.

In the immortal words of Mel Brooks, "Tragedy is when I cut my finger. Comedy is when you fall into an open sewer and die."

I had a job interview with a civil engineering firm many years ago when asking off-the-wall questions was just starting to come into vogue. So, in addition to the standard "What are your salary requirements?" and "What makes this company a good fit for you?" questions, one of the interviewers smiled and asked, "What brings you joy?"

Well, I couldn't exactly answer "schadenfreude" there, so I made up some half-true crap about the satisfaction of seeing my designs come to life and be taken for granted by the general public.

I didn't get the job. I guess I should have answered, "Sewers."

5 Like • Comment • View 4 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.