Complex Numbers (Book)

Blog Calendar

◄ October ► 2018
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 9 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!

Nov 14, 2024 at 2:04pm
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

October 31, 2018 at 12:22am

#944571

Atlantic City

I love depressing music.

To paraphrase the Doctor Who episode "Blink," "What's wrong with sad? It's happy for deep people."

I'm probably not all that deep, though. The things I like, they're mostly all right there on the surface: good food, good drink, money, movies, music, and video games. I'm no philosopher; I don't even have a liberal arts education, having opted instead for a very practical engineering degree.

And yet, when I hear a sad song, it makes me happy. I don't know why. I did notice on my first cross-country trip, years ago now, that my playlist is probably 75% songs about travel, the road, or cars. This has been true even before I spent days gripping a steering wheel, blinking into the setting sun, alone with my music and my thoughts.

But a good 90% of my favorite songs are what some people call "depressing" and I call "awesome." But hey, you already knew I was a Springsteen fan.

So like I said last time, I had to take an emergency trip to Atlantic City to hang out with an old friend who's going through a divorce. He needed it. I'd just as soon never go there again. See, I've been to all the classic gambling hotspots in the US: Las Vegas, Reno, and Atlantic City. Vegas is all about overdoing everything; it's exuberant and bright and it's like that rich friend you have, or would like to have, who laughs at everything, drives a Ferrari, and flashes a Rolex. Reno is... depressing. And not in a good way, not like the Tom Waits or Johnny Cash songs about the place. One time, driving through Reno, I spotted a billboard advertising a Morrissey concert. That's right; Reno is so depressing that they had to bring in Morrissey to cheer it up.

Atlantic City makes Reno look like Disney World.

Used to be, AC was the only place on the East Coast to gamble, so people went there from all over. Lately, though, Delaware, Maryland, Pennsylvania, West Virginia, Connecticut and even bloody New York have legalized gambling to some degree or another, which leaves Atlantic City with very little reason to exist beyond sheer inertia and classic Jersey stubbornness.

But they still have bars, and blackjack, and usually you can avoid the scam artists wandering in off the streets for long enough to let casino security kick them out. And, unlike Vegas or Reno, if you look out the window you can sometimes see the ocean, and forget for a moment that those waves will one day drown the city in a flood of sharks and used needles.

Sometimes the only purpose of a place is to remind you of how good you actually have it. Or - maybe - substitute "song" for "place" and now I might begin to understand my taste in music.

Everything dies, baby, that's a fact
But maybe everything that dies someday comes back.

2 Like • Comment • View 2 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.