Complex Numbers (Book)

Blog Calendar

◄ August ►
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:

Brandiwyn🎶

a day ago
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.

Aiva Raine

Nov 5, 2024 at 3:03pm
In response to "It's Hard Not To Scare"

Shaking head. Aside from the inevitable Simpson's spider goat song playing in my head which I will now share with you below, whenever I come across a story that has all these scientists doing ridiculous experiments for no logical reason, I must go- ah- scientists- CANCER? You do remember that problem right? Can we maybe cure that before we make cockroaches magnetic and elephants see pink elephants?

spider pig clip- and if you all now are singing the spider goat song- you're welcome! grin
https://www.youtube.com/watch?v=BARjPuUN36Y

1 Like

Aiva Raine

Nov 5, 2024 at 2:55pm
In response to "Anomalies"

One of your more humorous entries- I especially enjoyed- "Lofoten Vortex can be the name of my Bjork cover band."

Thanks for the laughs. Much appreciated.

2 Like

August 18, 2024 at 10:39am

#1075432

Revisited: "Challenge Complete"

Today's cruise on the river of time takes us back to the end of January, 2019. This was a 30 Day Blogging Challenge month, and for context, my current daily blogging streak wouldn't start for another ten and a half months. And, of course, it was before everyone's lives got disrupted.

The entry itself, "Challenge Complete"

, featured the kind of prompt I came to expect for the final entry into that challenge:

Write a list of at least 5 blogging prompts to add to the Challenge War Chest to be used for future rounds of the 30DBC. Then, use one of your own prompts to write your entry.

I've never really enjoyed coming up with prompts. Scratch that; I do enjoy it; it's just that when I'm expected to create one, my mind goes blank. I know this sounds odd from someone who's been judging "Invalid Item"

and therefore coming up with a prompt almost every week for nearly two decades, but there you have it. I just think of it as another challenge for myself.

The actual prompt list I came up with is uninspiring to me even now, and I won't quote it here. It's there at the link if you want. I'll just address some of the other things I said in the entry.

I don't know who coined the term "bucket list," and I can't be arsed to find out.

Unlike most words and phrases, they've traced that phrase in its "things to do before you die" sense to a precise moment.

I do know that it became the title of a moderately interesting movie with Jack Nicholson and God.

According to that link I just did, the phrase's origin and the movie title came from the same place.

While I've been known to use the phrase from time to time, I usually call it my "fuck-it list." This is because I've already done most of what I set out to do, and have given up on the rest.

Good to see my attitude hasn't changed in five and a half years.

It's come to my attention recently that life is much less frustrating if you can separate "things that I cannot control" from "things that I can control," and to focus on the latter while letting go of the former. This is something akin to the infamous Serenity Prayer, which I resent because a) it's a prayer and b) it's associated with AA, and AA is for quitters.

That's not my actual problem with AA, but it made a decent joke.

I've been walking every day for the past 5 weeks, which is, like, a new record for me for exercise.

I should have kept track of my record for "days without formal exercise." It'd be a lot longer.

Say I want to take a trip to space. How can I make that happen? Well, probably by paying Virgin Galactic a very large sum of money to fire me into a suborbital trajectory that technically takes me 100km up for a fraction of a minute, thus putting me, by definition, in space.

I think that particular venture never took off (pun intended). Branson lofted himself into a suborbital trajectory, but his maximum altitude was somewhat less than the accepted boundary of "space." Pretty sure I wrote about it in here at the time. Then Virgin declared bankruptcy. Or something. I can't keep up with all the rocketing these days.

Honestly, even if I were a billionaire, this would strike me as a colossal waste of money.

While I accept that other people wouldn't find it so, paying any amount of money for fame and bragging rights.

So here's the real example: I want to be published.

Yeah, not so much anymore.

Not much else of note. Kind of a boring entry, even now. Only one joke that I could find, and it wasn't even original.

Can't be "on" all the time, I suppose, but some challenges are never complete until the day you kick the bucket.

1 Like • Comment

© 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.