Complex Numbers (Book)

Blog Calendar

◄ March ► 2021
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

March 29, 2021 at 12:01am

#1007228

Totally Not Financial Advice

Let's take another crack at Cracked today.

5 Stupid BS Financial Things We Put Up With

Tell us how you really feel.

DISCLAIMER: None of the following is to be taken as anything even approaching professional financial advice. It's simply the griping of a grumpy millennial who will probably die without ever owning property larger than a nice couch.

Ooooh, look at Mr. Moneybags Millennial over here with the nice couch.

For a minuscule percentage of the population, their finances are something they enjoy looking at. They call their Swiss accountant every morning and say things like, "Read the numbers to me again, Quincy!" while chuckling over a mug of warm stem cells.

Okay, that's legitimately funny. Except that Quincy isn't exactly the first name I think of when imagining a Swiss person.

For the rest of us, opening our checking account app feels similar to cranking a jack-in-the-box that pops out and tells you you're eating noodles this month..

Sure, because there's nothing in the middle of these extremes.

Now there's no shortage of financial BS that starts from the top, raining lukewarm piss all the way down, like the fact that the federal minimum wage hasn't increased in over 10 years while the cost of living has gone up by 20%.

Well, they called it "trickle-down" for a reason.

And then of course there's the numbered list, because Cracked.

5. Modern Credit Scores Controling[sic] Everything

The credit score, for some reason, seems to have established itself as some sort of historical constant, despite the fact that the modern FICO credit score wasn't even established until 1989. Given the importance placed on it, you'd think the colonists showed up and started immediately issuing credit scores to the Native Americans along with their smallpox blankets. In reality, those numbers between 350-800 that decide pretty much anything you can do financially are probably younger than your parents.

Try younger than I am.

These days, credit scores are pulled basically every time you want to use a restaurant's bathroom, and unfortunately, they're here to stay. The best any of us can do is to generally try to think of our credit score as an ill-tempered romantic partner and try to minimize what we do to send them flying off the rails.

While it's probably true that the credit score has an outsized influence on everyday life, the article omits one of the main reasons we use standardized scores now: before them, you'd go apply for a loan, the lender would note your skin color, and assign creditworthiness in inverse proportion to its melanin content. This was, rightly, deemed unsuitable in an egalitarian society.

4. Useless Interest Rates On Your "Savings" Accounts

Provided you're one of the few that can actually afford to put any significant money into your bank's savings account and aren't hopping from paycheck to paycheck like a series of precarious stones, you may have noticed the abysmal interest rate offered by most.

Guy has a point here. However, the common reaction to seeing sub-1% rates on savings isn't "I'mma put this money into an index fund," but "I might as well spend it." This helps the economy and rich people. It does not help ordinary people, unless you only spend your money on locally-sourced, vegan, gluten-free, artisanal products, in which case you're not an ordinary person.

Now, I'm not poor, but I get excited whenever I see a penny lying on the sidewalk. There are those who feel that the effort needed to bend over and pick it up, combined with the potential for germification, makes it not worth it. I'm not one of those people. I pick that sucker up and put it in the back pocket of my jeans, and then wash my hands first chance I get. Also, I always forget about change in my back pocket, so they show up later, nice and sanitary, clinking around in the clothes dryer. Anyway, the point is, even a 0.1% interest rate is better than nothing, even though both 0.1% and nothing are below the rate of inflation. And you can find higher interest rates on savings than that.

And there's never been a more important time to sock money away than now; uncertainty is high and you might find yourself jobless, and you'll need something to tide you over whilst looking for a new job when the one you have dumps you for posting stupid shit on Twitter. The best thing to tide you over is money; your comics collection ain't gonna cut it.

3. 401(k) Replacing Pensions

Retirement plans at all seem like a luxury these days when it feels like the main occupation of the younger generation is three occupations. Millennials and Zoomers are lucky to get health insurance, much less realistic retirement options since Ublyft or Doormates or your employer of choice plans to ax you scot-free through their use of at-will employment as soon as you deliver a half-melted ice cream cone anyways.

While this has some truth to it, the real problem is that if a company does offer a pension, they'll lay you off before you're vested in it. The 401(k) and IRA plans are way more useful when the average length of time someone's in a job is approximately three days (Yes, that's hyperbole. I can't be arsed to look up the actual number, but it's low compared to the "entire career" our forebears "enjoyed.")

Because 401ks expose you and your hopes of a cabin on Golden Pond to the stock market in a way that traditional pensions do not. Anyone living in America over the last decade or so should be rightly distrustful of putting their future in the hands of the stock market, and indeed, we saw in grim relief what can happen with the recession decimating the 401ks of many citizens and forcing your grandpa to work as a Walmart greeter into his 70s.

Um... no. The stock market crashed hard in 2008. It reached a low point in early 2009. Since then, it's had the usual bumps and dips, but the overall trend has been upward. Of course, that won't last; as soon as the average person starts trusting the stock market again, it'll go bear and people will once again freak out.

Point is, if you just look at the last decade, it's been a bull market of historic proportions, and anyone who threw all of their money into it in 2009 could have seen a 600% return on investment.

Is it risky? Sure. So is keeping your money in your sock drawer where it's guaranteed to lose value due to inflation. The trick is to keep holding (and maybe even buying) through dips, and not selling everything when you hear the bear start to roar. Most people can't do that, and they end up selling low and buying high, the polar opposite of what they should be doing.

2. Banks Being Closed On Weekends

If you're someone with an aggressive work schedule, you've likely experienced the pain associated with finally squeezing a bank visit into your calendar, only to hear a discouraging "clank" as you finally get to the door of the bank. Even today a huge amount of banks are closed on weekends, making it difficult for those who work many hours to get anything done in person.

Okay, I get that this can be inconvenient, but really, who goes to banks anymore? The last time I set foot in one was sometime last year when I needed a notary public. And technically, it was a credit union, not a bank. A credit union that has Saturday hours. Seriously, the problem here is that people keep flocking to the major banks, whose primary goal is to fuck you.

1. Having To Prepare Your Taxes

Yeah, it's annoying, but what's the alternative? How about this one: you just get sent your forms filled out, check them, and sign them if everything looks good. That's not only NOT a pipe dream; it's already currently how portions of Europe handle taxes. So if that's true, why do Americans continue to take a math exam where a failing grade results in committing a crime every year?

Well, a big reason is because the people who help you take that exam have a pretty significant investment in keeping them complicated. Reporting from ProPublica shows that Intuit (of TurboTax) and H&R Block spent a combined $5 million in 2016 lobbying to prevent pre-filled returns from being offered to taxpayers. They then have the gall to pump out commercials starring an attractive 27-year-old from central casting that's never seen a W2 telling you about how they're here for YOU, to get you the MOST money from the big bad IRS because they are your FRIEND and they let you have half a bagel that one time, don't you remember?

This, now... this is legitimately enraging.

But hey, think of it this way: you don't really want to put everyone who works in the tax preparation business out of work, do you? Spend more money! Contribute to the economy!

6 Like • Comment • View 7 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.