Complex Numbers (Book)

Blog Calendar

◄ April ► 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 15 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 16 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.

April 19, 2020 at 12:07am

#981452

Top Bunk

One today from someone at my alma mater

https://aeon.co/essays/is-debunking-more-about-the-truth-teller-than-the-truth

Debunking debunked
Secular modernity requires the weeding out of all the baloney. Yet it’s not clear that we are any less credulous than before

What's not clear is that the goal was ever to make us "any less credulous than before."

Just as you can deworm a puppy, you can debunk a religious practice, a pyramid scheme, a quack cure. Get rid of the nonsense, and the polity – just like the puppy – will fare better. Con men will be deprived of their innocent marks, and the world will take one more step in the direction of modernity.

Read articles like this one, and the world will take one more step in the direction of postmodernity.

What we should imagine instead of an impartial skeptic is a person who gets a charge out of being the rational member of the exchange – someone who is drawn, for reasons that might or might not be clear to him or her, and that are probably difficult to articulate, to the drama of unmasking.

"And I would have gotten away with it, too, if it weren't for these meddling kids!"

There's really a lot more here, so much that my choice is to either quote it excessively or leave it at that. I'm choosing the latter because I'm lazy. But to summarize my takeaway from it, as I understand it, the author turns debunking into a social exchange, and skewers the idea of "modernity" (as defined by her) throughout. One could even say she debunks it.

My rebuttal? While it's not always easy -- or even possible -- to ascertain the truth of a situation, I think it's important to try. I agree that sometimes people go too far, perhaps by ascribing ill intentions to those they're trying to debunk. Maybe that's not clear; let me give you an example.

I had a friend who's a chiropractor. She spent many, many years at a school learning how to chiropract. It's her job and she makes a decent living at it, last time I checked. Meanwhile, many people consider chiropractic to be nonsense, a thing to be debunked. Someone like that might accuse my friend of lying, turning it on her instead of the practice itself. But she's not lying; she actually believes in what she's doing. Whether it's promoting falsehood or not, in her mind, it's truth. So no, she's not intentionally deceiving anyone, and I'm pretty sure that it would hurt her a great deal to be accused of being a con woman.

As for me, from what I can tell, there's some benefit to chiropractic, but many chiropractors' knee-jerk rejection of "allopathic medicine" is dangerous and a rejection of evidence-based treatments. Obviously, this didn't mean that we couldn't be friends, but it's not like her way would have helped me when I had a heart attack.

Sure did help with my back pain, though. (And yes, I'm aware that's anecdotal and not actual scientific evidence that it works, but that's not the reason I'm relating this.)

Point is, this article has issues, and if you want to debunk it yourself, go for it. Me, I'm going to have another beer.

3 Like • Comment • View 2 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.