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 21, 2020 at 12:05am

#993819

Out Of Control

What, me worry?

PROMPT September 21st

One thing outside of my control that I need to stop worrying about is...

I'm... not really the worrying type.

As the prompt suggests, there are things in my control and things that aren't. If a situation is, at least in part, in my control, then I tend to do something about it. If it's not, then I figure out a way to deal with it -- usually by imagining the worst possible outcome, mentally preparing for that, and then being relieved when it turns out to be not as bad as I expected.

Of course, like everyone else, I have certain concerns. No point worrying about them, though. It's a waste of brain power, when that brain power could be used to play video games or get distracted with booze.

I'm sure there are a lot of things on everyone's mind right now: pandemic, economic struggles, upcoming election in the US, social issues, the impending end of Western civilization, and all the other joy that 2020 has brought us. Hell, I was just reading where archaeologists found a bunch of sarcophagi

in Egypt. I mean, I'm a rational guy, but unearthing cursed mummies in 2020 sounds like a Really Bad Idea, and these archaeologists probably should have watched more horror movies before proceeding.

Point is, there's not a damn thing I can do, and if there were, I'd be doing it instead of turning it over and over in my mind. It's not like I can fly to Egypt and ask the archaeologists what the hell they were thinking, and even if I could, it wouldn't do any good.

In case it's not obvious, I'm joking about the mummy curse thing; it's a worn-out horror trope, which makes it ripe for comedy. Jokes are what keep me from worrying. I haven't found many situations yet that I couldn't joke about. Hell, I was getting treated for a heart attack, watching my ticker beat on the screen, millimeters away from possible death, and all I could say was, "Huh... it's not made of stone after all."

If you can't control the situation -- and much of the time, you can't -- you can control your response to it. I recognize that worry is one of those emotions that's really hard to address, but just because I can't control something doesn't mean I'm going to let it control me.

Usually, though, it's not about control, but about just letting go. I don't accept that everything's in some higher being's hands, or has a purpose. Also, there's no telling what the future will bring; could a situation come up where I do start to worry? It's possible. It's just not happening right now, and I'm certainly not going to worry about getting worried.

9 Like • Comment • View 12 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.