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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:

Kåre Enga in Montana

about 12 hours ago
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

about 17 hours ago
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

a day ago
In response to "Butt Of Course"

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

Talk about retaining water...

2 Like

Elisa the Bunny Stik

May 1, 2024 at 10:53am
In response to "Mad as Hell"

"But if you want to really see how anger is useful, you need to consider how it's used as a tool for manipulation."

This is a line that must be regarded with care. After all, there are people that get angry about the way they are being treated on a large scale and harness that anger to change their circumstances. There is some level of manipulation in this angry but still legitimate flavor of activism. We do have to consider the possibility that this angel's usefulness can have net benefits (such as environmental cleanup and protection; see the Live Canal as an example).

GeminiGem survived GoT

Apr 29, 2024 at 1:53pm
In response to "Supplementary"

Working in health care for a zillion years, I've heard it all. The whole thing about something being natural, therefore it would be good for a person is very, very, very...very prevalent. An internist I worked with had a fantastic comeback to that line of thinking. She would say, "Arsenic is natural, are you going to start taking that?"

1 Like

Lazy Writer est 4/24/2008

Apr 28, 2024 at 2:14pm
In response to "Revisited: "Exercise""

I will be 75 in July. My stepdaughter gave me a bike because I wanted to ride it again. Well, I started off shaky and stayed shaky...then I fell off it...A passing motorist stopped to help me get up...I have NOT been back on that bike and will not ever again.

🌕 HuntersMoon

Apr 28, 2024 at 10:43am
In response to "Revisited: "Exercise""

So, you're saying that now you pedal your ass differently?

Elisa the Bunny Stik

Apr 27, 2024 at 10:33am
In response to "Pleasure and Pain"

it illustrates why it's important to have people from different backgrounds, with different worldviews, working on scientific research.

This right here is why I get rather irritated by people poo-pooing college these days. I feel like that attitude effectively shits on minority populations that may not have strong finances but do possess persistent curiosity and want to learn about various subjects in-depth. In the 90s, these groups were exclusively told to go to trade schools even if they had the aptitude for college education. Nowadays the blanket "Everyone should consider a trade" mantra employs a more subtle (but still abundant) form of discrimination. I'm so over it.

1 Like

Kåre Enga in Montana

Apr 25, 2024 at 3:16am
In response to "Going to the Dogs"

I have ants in Thailand. Will I miss them in Montana? No.

Would it be nice to have a cat and a dog, here or there? Yes, but I have struggles keeping my neglected plants alive.

Not every situation is suitable for everything or everybody.

Kåre Enga in Montana

Apr 25, 2024 at 3:09am
In response to "Tipped Out"

I don't tip. In my travels I rarely find tipping the norm.

I also don't haggle.

When you add the tip... the true cost of America becomes evident. But what would I know? I travel while others who have double my income can't pay rent.

August 17, 2021 at 12:01am

#1015729

Fence

Okay, so today's article is about one particular life decision, but it seems to me -- someone who is not well-versed in psychology -- to have other applications. So here it is.

I help people decide if they want to have kids. Here’s my advice.
A parenthood clarity therapist explains how she helps fence sitters make one of the most important decisions of their lives.

I made that particular decision long ago, though I understand that the pressures and consequences tend to be different for women. But once I realized I did have the power to make the decision, it was an easy one. The trick was avoiding the societal pressure to conform to a particular life script.

I’m a therapist who has dedicated my life to helping people figure out if they want to have children. I’ve been doing this for 30 years and have seen more clients than I can count of all stripes — men, women, single, married, and partnered people. People just out of a relationship and people just starting a relationship. People from ages 28 to 59. Our goal is to help people make possibly the biggest decision of their lives: whether or not they want to become a parent.

Apparently, questioning that life script is more common than I thought.

Many assume that a time will come for each of us, at which point we’ll “just know.” Even though that is the case for some, it’s a myth to think it’s that way for everyone.

Yeah, I think I can pinpoint the moment when most people "just know." By then, it's too late, and you're committed.

From desperation, they have to make a decision. Fear instead of desire runs the show. Operating on fear is a lonely, excruciating process that leaves many immobilized. But when a decision is made from a place of desire, joy, or clarity, the experience is quite different.

That's the key bit that I think might be more generalized.

The article goes into some shrink-rap type exercises, which, to be honest, I skimmed.

Now, I don't want people to get the idea that I'm proselytizing my own point of view here. Personally, I think the world would be best off if everyone who wanted children could have them, and everyone who didn't want them, didn't. From my perspective, if you're going to worry about regrets one way or the other, it's better to regret not having kids than to regret having them. I mean, consider what that attitude could do to a child, even if you never say it out loud. (Of course, it's best to have no regrets, either way.) But often, parents press their decision on others: "It's so rewarding! You'd be missing out on such joy! You'll never know what real love is!" All I'd say to anyone on the fence is: don't listen to those words; look at what their lives are like and decide if that's really what you want. And pay particular attention to any sentence that begins "I love my children, but..."

But anyway, like I said, that's not the only major decision people will make in life. For example, should I have beer tonight, or scotch? Or maybe both? Likely I'll decide it at random, because then I can blame the random number generator if things don't go as well as I hoped.

6 Like • Comment • View 5 comments

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