Complex Numbers (Book)

Blog Calendar

◄ September ► 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
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 3 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 5 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.

September 28, 2020 at 12:06am

#994431

Baggage

I'm pretty damn possessive of my possessions.

PROMPT September 28th

If you were forced to eliminate every physical possession from your life with the exception of what could fit into a single backpack, what would you put in it?

1) My laptop, its power cord, mouse, mousepad. Can't live without these things. Why do I have a mouse when I have a laptop? Because I can't stand using the damn trackpad, and besides, how can I game with the trackpad?

2) A metric assload of $100 bills so I can buy more stuff. No, I do not consider this cheating. Money is a possession, and while most of it's just numbers on some bank's balance sheet, I can convert it to a physical possession during business hours.

3) A .45 caliber handgun for when I find the sonofabitch who "forced" me to give up the rest of my possessions, which include somewhat valuable houses that won't fit into any backpack I've ever heard of. I mean, I'm not a violent person, but that could change in the above scenario.

I guess that last one is kind of cheating because I don't currently own a .45, but that's the first thing I'd buy with some of the money.

4) My passport so I can leave the country after retiring the person from (3).

Seriously, though, the only plausible scenario wherein I could see this sort of thing happening would be an imminent natural disaster, like a hurricane or tornado. We don't get many of either in the Virginia Piedmont, but it happens. It's rare enough that I haven't been arsed to put together a dedicated bug-out bag, which is really something I should work on doing, you know, just in case.

Wouldn't really need the cash, because of cards and such, but the laptop is truly essential. And no, there wouldn't actually be a gun involved unless the reason was a zombie invasion, which happens even less often than hurricanes or tornadoes. The passport is for real, though, because it would suck to lose everything and also not have a means to leave the country if I have to. My wallet would go in there, too, except that it's probably in my pocket. Same with my Android.

Unless civilization has completely collapsed, I wouldn't even bother with toiletries or clothing or whatever -- those things are readily available, though I'd miss a few of my T-shirts. If civilization has completely collapsed, though, not much use for the laptop or smartphone, either. And why would anyone assume I'd survive such an event? I'm not the survivalist type. And without a functioning CPAP, I'm not long for the world anyway.

If the point of this exercise is to get us to think about what physical possessions are truly essential in our lives, I guess what that comes down to for me is: money. It's just so damn versatile.

But I do like the laptop.

8 Like • Comment • View 6 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.