Complex Numbers (Book)

Blog Calendar

◄ November ► 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
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!

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

a day 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.

November 3, 2019 at 12:41am

#968863

Wait for It...

PROMPT November 3rd

Write about a time when you waited a long time for something. Did you end up getting what you wanted? Was it worth it?

Well, there was the time I went to the DMV one morning, and left three years later with a driver's license...

Okay, I'm exaggerating a bit, but it felt like three years.

There's a brewery in Richmond, VA called Hardywood. They've since expanded into other locations, including one right here in my town, but at one point they just had the one location in an industrial park about an hour's drive from me.

Now, there are breweries all over Virginia, but this particular brewery made a gingerbread stout that was, at the time, the only beer to ever get a perfect 10/10 score on a popular beer rating site. Not only that, but I'd had the opportunity to sample it and it was, indeed, delicious. So, naturally, I had to have some. Also naturally, so did every other drunk in Virginia, and let me tell you, we are fucking legion.

To further set the scene, this particular beer is a seasonal offering, not available year-round. As you might be able to tell from the name, it's winter-holiday-themed. That means it came out in November. If you don't know anything about November in Virginia, I can sum it up in two words: it sucks. Cold, but usually not cold enough to snow. Often rainy. Rainy is fine. Cold is fine, to a certain extent; at least, I'm used to it. Cold and rainy... it sucks.

So it was that on the cold and rainy November release day for Gingerbread Stout one year - I dunno, maybe 2013? It's been a while - I found myself and a friend standing in line outside the enormous Hardywood brewery in Richmond, waiting to claim my allotment of just two bottles (albeit 1L bottles) of sweet nectar of the winter gods. Along with every other drunk in Virginia. The line snaked from the brewery door, out to the street, and around the block. As a reminder, this is an industrial park block. In the rain. In the cold rain. In the nasty Virginia November cold goddamn rain.

We waited. The line inched forward. It rained. It colded. The line inched forward. The day stretched on into eternity.

(insert elevator musak here)

(pause for effect)

Finally we got our bottles and booked out of there.

Was it worth it? Oh, definitely. Since then they've increased production and one can often find this paragon of beer in local stores, so there's no need to go through that again. At the same time, however, it's not quite as good as it was the first few years. Delicious, yes, worth buying, certainly, but I wouldn't wait in the - did I mention cold rain yet? Because it was cold and rainy - cold rain in an industrial park for it again.

Now, it may seem strange that when prompted for something I had to wait a "long time" for, I pick something that I had to wait, max, a few hours for. This is because I don't wait. I'm not a patient person. If I do find myself waiting for something, I distract myself - games, reading a book, whatever. Can't do that in a cold, rainy, outdoors queue. So, say, waiting for my passport or tax refund or the latest Brandon Sanderson book that I preordered from Amazon months before it's due to come out - well, I don't count those as waiting, because I'm doing other stuff.

Also, beer is important.

5 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.