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Friday, May. 10, 2024

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

Annette

about 12 hours ago
In response to "Meditation Clause"

Everytime a stranger asks me to close my eyes, I keep my eyes open to see what they are up to.
Meditation is not for me.

But I think most people would have 45 minutes every day if they took that time away from social media or TV watching.

2 Like

Wordsmitty ✍️

a day ago
In response to "Super Stew?"

But . . .

What's the difference between one being in the soup or in a stew? Is one thinner or thicker? How do writers use soup and stew?

1 Like

Elisa the Bunny Stik

a day ago
In response to "Super Stew?"

"Served in a pot? Maybe in your country."

Honestly, in the US I'd think soup would be served in a pot due to the quantity that ends up being consumed.

1 Like

Lazy Writer est 4/24/2008

May 8, 2024 at 3:02pm
In response to "Be Positive"

Mine always tell me to eat more fruits and veggies.

Annette

May 8, 2024 at 10:52am
In response to "Be Positive"

Asking doctors for advice has its own pitfalls. Because there is no money in recommending a sensible nutrition pattern, they will say things like: Look it up online.

2 Like

🌕 HuntersMoon

May 5, 2024 at 8:50am
In response to "Revisited: "Fail""

Shame on you for making fun of the Hoggs. Being a Virginian, Bob, you should know the reverence that the name Hog inspires recalling the glory days of the Washington Redskins (now the Commanders). The Hogs

1 Like

Charity Marie - <3

May 4, 2024 at 5:42pm
In response to "Overdraft Dodgers"

I have four different accounts and each one has a purpose. Savings, personal debit card, auto draft debit card, and a b8lls account. The bills account is the only one that can overdraft as it's for manual big bills like rent, cell, electric, etc. Stuff that mist be paid. The rest are blocked from overdraft and the savings account has no debit card attached. My bank accounts have been hacked too many times so I keep it this way to protect myself. It is very rare I ever pay an overdraft. I have a money market account for money greater than $10K so it gains interest and isn't touched except emergencies. That is a secure account too.

1 Like

Kåre Enga in Montana

May 3, 2024 at 4:23pm
In response to "It's a Crime"

Thailand versus Montana versus New York versus Costa Rica.

Theft? Not in Thailand! Not a huge concern in Missoula, perhaps in NYC, definitely an issue in Costa Rica.

Violence? Not a huge concern in Thailand. More so in MT, NY and CR (where it wasn't a concern years ago), definitely a problem in Saint Louis and the US in general. El Salvador is known for violence.

Death by vehicle. Not a huge concern in either NY or MT. A rising problem in Costa Rica. Thailand is one of the worst places in the world in this respect.

You may be shot and killed in parts of the US but you're more likely to be run-over in Thailand.

1 Like

Simply Me

May 3, 2024 at 11:58am
In response to "It's a Crime"

I get it. The fear spreading jerks wants us to have an "us vs. them" attitude. The division gives them leverage. (they think)

1 Like

🌕 HuntersMoon

May 2, 2024 at 11:37am
In response to "Butt Of Course"

My wife tried waterskiing once... called it the 100-yard douche.

Talk about retaining water...

2 Like

September 7, 2019 at 12:03am

#965734

Reflection

PROMPT September 7th

Reflect on WDC’s 19th Birthday week! I don’t know any other online community that celebrates like we do

What was your favorite activity to participate in? What is the favorite thing you wrote? What is the favorite thing you read? Did you win anything? (or hope to?

) Tell us!

Yeah... honestly, I didn't do as much as I'd hoped. I've been trying to write at least one contest entry a week all year, but none of the prompts I saw really did it for me, this time. Most of them were about birthdays, and at my age, that's not something I care to think about. Except, of course, when it's my birthday, at which point I want ALL the presents.

So now I'm behind on that. I'm sure I'll be able to catch up, though.

Hey, that's odd. Usually, that sort of thing makes me give something up as hopeless. Maybe I have changed.

Anyway, I was glad to see all the participation. This is a unique venue, as the prompt above alludes, and I like to see it thriving.

Next year is the 20th. Because we're programmed by society to give greater emphasis to numbers that end in 0, I expect that'll be an even bigger deal.

A slightly pedantic aside:

I've seen references to something's nth year. Usually, in context, it goes something like this:

"Jack is 50 years old."

"Amazing! He made it to his fiftieth year!"

While technically correct, if Jack is 50 years old, that means that he also made it to his 51st year.

That sounds odd sometimes, but just think about it: When was your first year? Chances are you don't remember it, but your parents did. They measured your age, then, in months. When you're born, you're 0 years old. A year later, you're 1 year old. In the meantime, you're in your... first year. Consequently, your second year stretches from your first birthday to your second birthday, and so on. When you're 10, you're in your 11th year of life. It's like with centuries: we're in the 21st century, and all the years start with 20.

Put another way, right after you're born, you're not in your 0th year.

You're 29? Then you're either lying, or you're in your 30th year. You can tell someone "I'm 29" or "I'm in my 30th year." The latter will make people think you're 30, because they haven't read this blog entry, so don't do that if you have a youth vanity thing going on.

Point being, as of right now, WDC is in its 20th year, and that's an amazing feat for a relatively small online community.

4 Like • Comment • View 2 comments

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