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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 Udon Thani

a day ago
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 Udon Thani

a day ago
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.

Kåre Enga in Udon Thani

a day ago
In response to "Reality Cubed"

My dreams may be different from your dreams but if we share them with others then some form of the dream may live on. Regardless, if we don't eat we die. "Joy gives us wings." "Reality bites."

Aiva Raine

a day ago
In response to "Tipped Out"

Agreed. I'll tip and well, for actual waitstaff at restaurants. I'll tip appropriately for bell-staff who assists with luggage at hotels, the more luggage, the bigger the tip. I'll give a tip to the valet as well. Beyond that- I don't tip. Certainly no tip for the fast food workers, coffee baristas, grocery store clerks, etc.

It annoys me to no end that we're being asked to tip for all kinds of jobs where they are being paid an hourly wage. I've worked as a waitress when I was young and my daughter currently does. In those jobs- she absolutely depends upon proper tipping to make a decent wage. And I hate the fact that she is dependent upon tips to do so.

It leaves women especially at the mercy of arsh**() on whether she wants to accept hostile, negative, sexist, harassing, demeaning, and negative behavior from her customers in order to make a living. It condones people treating their waitstaff like shite in order to get paid. While there is much improvement from the 30 years ago when I was working as a waitress in the skimpy outfits we were forced to wear- it's still an issue at non-chain, independent owned restaurants and diners.

Women are left to the mercies of jerk customers and their only recourse is the manager who they have to hope supports their waitstaff rather than the jerk customer. Tipping should be eliminated. All employees should be paid a livable wage and waitstaff especially should not be dependent upon tolerating crappy to obscene behavior from customers in order to make a living.

But, until that happens- I always tip at least 20% and often times more. Very rarely have I tipped lower and the service in those situations was abysmal and they still got 10%.

1 Like

GeminiGem of House Lannister

Apr 23, 2024 at 6:51pm
In response to "Going to the Dogs"

I don't understand the intersection, either. I lived in a much smaller city and found that having dogs was a hassle (although it didn't stop me), what with the complainey neighbors, the extra licensing, etc. I live in a rural location now and it works great. I can't wrap my head around living in NYC with or without a dog, although I like the idea of a place that issues a canine and supplies upon moving there. Can that please be a thing?

1 Like

Lazy Writer est 4/24/2008

Apr 23, 2024 at 3:31pm
In response to "Going to the Dogs"

I love my little dog...but I live in a biggish house with a fenced backyard.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:14pm
In response to "That's Cole"

I knew and ate Kohlrabi before I ever heard of kale. Kohlrabi is so much better in every way.

That last quoted sentence is hilarious. I am glad that I wasn't bred to be a Brussels Sprout.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:11pm
In response to "Cash Stash"

The discussion of money is an interesting one. Remember the recent collapse of a few banks? I think it was about a year or so ago?
Yes, deposits were FDIC insured up to $250,000 per depositor. But some people and companies had more money in that bank than the FDIC was insuring.
I never followed up on what happened to those people. I don't run in circles of people who own that much cash.

My accounting professor took half a period to explain to us what happened and how the bank went from Silicone Valley darling to dead so fast.

He also told us that the value we give money is not backed by anything except our hope and faith that our economy will keep going.

We didn't discuss whether the value of money needed a lower income class of people.

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 3:04pm
In response to "Revisited: "Hack This""

In my last psychology class, we discussed the evolution of the brain. It is now settled science that we evolved to have not only larger, but also vastly more powerful brains than most other animals because we learned how to cook (process) our food.
Although we are only about 1/4 to 1/3 of a normal gorilla, we eat half of the calories in a day. Not only that, we prepare the food in a way that we get to use more of the calories that we ingest.
The result is that our brain takes up more space in our noggin than a gorilla brain takes up in his noggin. Not only that, each of our brain cells is smaller, so we can fit exponentially more of those into our head.

Now, using all that goodness ...

1 Like

Aennaytte: Free & Wild in GoT

Apr 23, 2024 at 2:58pm
In response to "Hope for Hops"

Wait! Why are beer and coffee affected by climate change? That wasn't supposed to happen. All we had to do was have a boat by the side of the house for when the sea levels rise and beg our property insurance to cover fire damage. How are we supposed to remember all of that if we don't get coffee to wake us up in the morning so that we can think and beer at night to dull our sense of doom?

December 29, 2020 at 12:02am

#1000975

Cold Moon

"30-Day Blogging Challenge ON HIATUS" [13+]:
29. December Full Moon (aka Cold Moon)
Write something about the full moon.

Dammit.

We really, really need to stop associating full moon names with Gregorian calendar months.

The concept of naming full moons evolved separately from the Gregorian calendar and its predecessor, the Julian. The folklore associated with moon phases was tied to seasons; that is, equinoxes and solstices.

The Cold Moon - or whatever it's called in whatever culture - was the first full moon after the winter solstice in the Northern Hemisphere (hence "Cold"). This has an approximately 1/3 chance of occurring in our December, and about a 2/3 chance of occurring in January.

I know I've ranted about this sort of thing before, in connection with the "Blue Moon." It's as if the internet just doesn't pay attention to a single word I say...

...which is fair, I suppose, since I'm basically nobody.

It's still the hill I choose to die on.

Once more, with feeling: there will usually be three full moons between equinox and solstice, or vice versa. On those rare occasions when there are four, the third of the four is the Blue Moon. "Rare" meaning about once every three years or so; hence the expression "once in a blue moon."

There was a time, some few years ago, when we had two full moons in January, none in February, and two again in March (January and March having 31 days each by fiat). This all by itself should have been sufficient to stop this "second full moon in a calendar month is a Blue Moon" nonsense, but apparently that was not the case, as the wrongness persists to this day.

And again, the method of naming moons relative to equinox/solstice is independent of whatever calendar is being used, so it is more universal.

An astronomer I'm acquainted with, Phil Plait, accepts that either method is "right," because like it or not, the Gregorian calendar is what we're stuck with, at least for now. I have a great deal of respect for Phil; I spent a week in a cabin in Colorado with him and his wife and a few other people. I think I understand his reasoning for that; as with a dictionary, it's a matter of descriptive versus prescriptive, and from his point of view anything that gets people interested in looking up at the sky is a Good Thing.

I agree with that bit: if you can be arsed to get out of your warm house in December or January (again, I'm being Northern-Hemisphere-centric here) to look up at the Moon in all her glory, that's great. Do it. Or if you spend a week in Colorado looking at the sky, preferably during a time when there is not a full moon because without the competition, and also preferably in the company of a professional astronomer who can show you shit through a telescope that's even more amazing, the rest of the sky can be even more glorious.

Where I disagree with Phil is that I believe we can't just abandon the folklore; trying to fit it into modern timekeeping is, to me, a bit like trying to hammer a round peg into a square hole. Or maybe it's the other way around; whatever. Doesn't matter; point is it's not going to fit right no matter what you do.

And honestly, I'm of two minds regarding calendar reforms. Personally, I think we should either go back to a purely astronomical one, where solstices and equinoxes mark the seasons but the moons are tracked as per one's chosen folklore; or abandon the concept entirely in favor of something like the Tranquility Calendar

.

Still. Go look at the full moon, if weather conditions allow. I know it happens every 29 days or so, but it's still worth noting.

7 Like • Comment • View 6 comments

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