Complex Numbers (Book)

Blog Calendar

◄ February ► 2022
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
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 8 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 10 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.

February 22, 2022 at 12:02am

#1027192

It Snuck Up On Me

It's been a while since I talked about the weirdness of English. This Cracked article delves into a particular linguistic idiosyncrasy that's bugged me for a while now.

The Strange History Of 'Sneaked' And 'Snuck'

No countdown-numbered list this time; just a straightforward discussion, though with the usual humorous twists. The article itself is from last month.

We asked readers their least favorite thing about traveling for the holidays. We received a wide variety of answers. Martha C. said, "People." Kurt W. said, "People." Crystal H. said, "People," while James F. Michael H, and Dwardo L. all said, "PEOPLE." Graham H., on the other hand, said, "Other people."

I must concur.

Some readers offered different answers, however. Fred F. said, "Traveling." Tim K said, "Traveling." John K. said, "Traveling," Edwin O. said, "Traveling," and Dwight C. said, "Traveling, lol." Aimee M. and Alan K. said, "Traveling." Brendan D. and Jim D. said the worst part about traveling for the holidays is "Traveling for the holidays." "Having to travel for the holidays," said Robyn M., while Michael R. said, "Traveling for the holidays."

There's a simple solution to all of this, you know. It's tough even for me, but all you have to do is... not travel.

So, instead of talking about travel, let's move on to something that does interest readers: grammar.

Worst segué ever.

Recently we talked about how An Injured Teen Sneaked Back Into WW1 By Cross-Dressing As A Nurse At A Dance and A Woman Sneaked Her Boyfriend Out Of Prison In A Dog Crate. Both times, readers wrote to us, saying that "sneaked" is not a word—the word we were looking for is "snuck."

Again, I concur.

Sneaked is correct; all dictionaries and grammarians agree on that. Snuck has also become acceptable.

As I've mentioned numerous times, dictionaries are descriptive, not prescriptive. That is, dictionaries reflect common usage, rather than dictate from on high what the common usage should be (we're not French). Part of the fun of being a writer is coming up with one's own words. If you're lucky, they'll catch on. Just stop trying to make "fetch" happen.

Merriam-Webster describes snuck as originally a "dialectal and probably uneducated form" of sneaked.

When I was a kid, teachers tried to correct us every time we used "ain't." "Ain't ain't in the dictionary," someone once told me. I don't think anyone these days would bat an eye if someone said "ain't," but it used to be a big deal. This proscription was slightly racist and definitely classist; no one's going to use "ain't" in a research paper (unless it's researching oddities of language), but at least here in the American South, we use it in conversation quite often.

Snuck makes sneak an irregular verb, and while English has lots of irregular verbs, it nearly always evolves the opposite way: Irregular verbs gain regular forms, which eventually edge out the irregular form. That's because people (including those supposedly uneducated ones who first came up with snuck) find regular forms easier.

I found out fairly recently (considering that the word was only coined fairly recently) that the past tense of "yeet" is "yote," not "yeeted." This makes that lovely linguistic gemstone even more shiny to me.

It's worth noting here that Urban Dictionary

contains the following analysis of "yeet:"

When you apply 80%+ of the relative maximum possible impulse to an object upon propelling it from your hands.

Notes:
-The maximum possible impulse is RELATIVE to what your maximum is (if you were to use the general maximum, any impulse would be ~0% of the maximum, as the maximum is now infinity). Your maximum is defined to be the largest impulse you can exert on the object.
-Any object propelled with less than 80% of the maximum possible impulse is considered to be thrown, and not yote.

My notes:

1) They should be using "force," not "impulse." Impulse is the integral of force over time and I just lost half my readers.
2) In order to reach infinite force, one must apply infinite acceleration (because no amount of acceleration will budge infinite mass and the formula is force = mass * acceleration, according to Newton). Good luck with that.
3) Note the proper use of the past tense of "yeet" in the explanation.

But of course I digress. Back to snuck.

They can't be confusing it with some other word similar to sneak that takes a past tense of -uck, since none exist. Though, we can think of some similar words like stink and sink that have past participles with that form.

Close enough.

Though, if the pair wanted to argue further, Jennifer could have said that dictionaries are descriptive not prescriptive...

Good to have my assertions validated by a comedy website.

...and just because a dictionary records a certain usage doesn't mean it's right.

Truth. No amount of arguing will, for example, convince me that the word "bromance" should exist at all, let alone be acknowledged by a dictionary.

Sadly, the Cracked article doesn't delve very deeply into the question of exactly why "snuck" is a legitimate conversational past tense of "sneak." My personal theory? Like most words ending in -uck, it's just plain fun to say. Still, no one uses "puck" as the past tense of "peak," as in "He puck in high school and it's been downhill for him ever since."

Now if someone could explain to me about "dreamed" and "dreamt," that would fill another gap in my knowledge. But I have a limit on how much I can be arst to look up in one day.

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.