Complex Numbers (Book)

Blog Calendar

◄ July ►
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🎶

about 21 hours 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

July 18, 2024 at 12:31pm

#1074113

All In a Row

Got another "Journalistic Intentions"

[18+] entry today:

Jessica Fox

When it comes time to write on a subject about which I know next to nothing, my obvious first stop is Wikipedia.

Sure, it's not perfect, but is anything? Earning a gold medal in the Olympics is about as close as one can get.

And I do have respect for anyone talented and dedicated enough to do that. I also have respect for the talent and dedication required to be an opera singer, but that doesn't mean I want to subject myself to the experience of sitting through an opera.

As much as I enjoy learning new things, there's just not enough time to be interested in everything. Some things get pushed to the bottom of the queue, like opera or sports.

So while it may shock some people that today is the first time I've ever heard of Jessica Fox, today is the first time I've ever heard of Jessica Fox.

Would I have heard of this medal-collecting canoeist—that is, would some news story about her have impinged itself on my consciousness before now if she were from the US instead of Oz? Maybe. Maybe not. If so, that wouldn't be my fault. A lot of the news I get is from the US, but I also get information from international sources, and it's not like she's from some obscure country with a weird language. Okay, weird language, sure, but Australia is hardly obscure. In any case, I actively avoid sports reporting. It's a practice I inherited from my parents.

I'm sure it's somehow bad that my first thought was "sure, you pretty much have to be an Olympic athlete to outrun/outswim/outrow the local wildlife there." That's gone past the "tired old joke" phase to "always funny." It's especially funny because I'm pretty sure Australians promote the exaggeration in order to keep ugly Americans from wanting to visit.

It's not working on me. I'd love to visit, drop bears and all. The thing that's stopping me is the thought of a 24-hour-plus flight (with connections) cooped up in a flimsy aluminum can with a bunch of American tourists.

For shiggles, though, I just looked up some flights (I had to in order to confirm the duration), and the prices are remarkably reasonable. For riding steerage, anyway. Less than 2000 US dollars for a round trip with one stop. Yes, that's a lot of money, but not bad for flying nearly halfway around the Earth, which, I feel I must reiterate, is round.

But I digress. Remember up there I said I inherited an aversion to sports news from my parents? Apparently, things like that run in the family, because Fox's parents were also world-class paddlers.

I guess you could say they're all in the same boat.

4 Like • Comment • View 3 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.