Complex Numbers (Book)

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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/

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10 Most Recent Blog Comments:

Elycia Lee ☮

about 9 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 22 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

a day ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

January 10, 2020 at 12:04am

#973073

A Day in the Life

PROMPT January 10th

What are some of the routines you follow in your daily life? Do you typically stick to your routine, or do you prefer more spontaneity?

Bit of both.

I've said before that there's nothing I do on a daily basis. For example, while I try to write in here every day, there's a glaring hole in my December records that represents my trip to California and recovery therefrom.

The closest I get to a daily routine is about as basic as stuff gets: eating and sleeping. My current meal plan involves six small meals per day - but I skip occasionally, again due to travel. More, smaller meals works for me for weight loss; it keeps me from getting too hungry. If I manage to hit my goal weight, and I'm under no illusion that I can be any more successful at that than I am at anything, that will probably change. And while, like most people, I tend to sleep every day, it's not on a fixed schedule; I have the luxury of going to bed when I feel like it, again with a few exceptions.

One thing I have managed to do on a daily basis is language lessons on Duolingo. In an attempt to keep up a streak, I've managed to at least do a few lessons every day since late August. Until I've been at that for a year, though, I can't say I do it every day.

And then there's exercise. I try to hit the gym every day, but some days, especially when traveling, I just walk for half an hour or more. Rarely, I just don't have opportunity for any dedicated exercise. But I'm determined to not make excuses, so probably 99% of the time, some sort of exercise gets done. Someday, I will fail. Today is not that day.

As for spontaneity, I find that difficult on a daily basis now, but it manages to crop up sometimes. The problem is that most "spontaneous" things I want to do involve calories (e.g. food or beer), so I've forced myself into a schedule to help me stay on track. But when I travel, I often pick things to do and see at random.

Contrary to popular belief (one that I, admittedly, foster), I don't drink every day. Well, water, yes. And Crack Zero, certainly too much. But alcohol consumption is maybe once a week at most.

So, when I'm home, and there's nothing particular scheduled, it goes something like: Wake up whenever; shower; breakfast; cat feeding; language lessons; second breakfast (thanks, J.R.R.); exercise; lunch; other obligations; nap; cat feeding; snack; entertainment; blog; light dinner; reading; late-night snack; sleep. Repeat as necessary. Somewhere in there, I find the time to hang out here and keep up with other things on the internet.

You'll note there's no "work" involved; being retired has its benefits, and besides, work was interfering with my video game time. When I was working, I barely had time to get anything else done. You think it takes 8 hours, but it always ended up being way more than that, especially when I was running the show.

And yet, I never seem to have time to do everything I want to do, or "should" do. I find this frustrating. But I guess that's what life is: compromise.

Woke up, fell out of bed
Dragged a comb across my head
Found my way downstairs and drank a cup
And looking up I noticed I was late
Found my coat and grabbed my hat
Made the bus in seconds flat
Made my way upstairs and had a smoke
And everybody spoke and I went into a dream

8 Like • Comment • View 10 comments

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