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 1, 2020 at 2:21am

#972350

Decade Dance

PROMPT January 1st

Welcome to 2020! As we start a new decade, take the time in your entry today to look back on the previous decade (2010-2019). Write about some of the major milestones from the past ten years. When you look back on your life over the past decade, what events stand out as most noteworthy and significant?

For me, the Teens are a lost decade.

My father died in the late noughties. That was a watershed moment for me. Shortly thereafter, my wife dumped me like yesterday's trash. So i started drinking in earnest.

And I just spent the last hour going through old blog posts, trying to remember what was going on 10 years ago. Damn, I was an asshole. Also, I was funny. Funnier than I am now. This sucks.

The thing that stands out for me over the past decade was traveling.

In 2010, I bought my current car, a Subaru Legacy. It's got 99,000 miles on it, give or take. Most of those miles were from driving across the country. Not once. Not twice. Not even three times. I've made four cross-country trips. I think. I've been drinking (quelle surprise) and I may have lost count.

Let's see. There was the first one, where I got it in my head that I would go from the easternmost point to the westernmost point in the continental US. Okay, go ahead, get pedantic and say that Alaska is on the continent. Fine. You know what I mean, though. I drove from Maine to Washington State. It took a couple of weeks, because I took my time.

There was also the one where I picked three points in the US at random. There was one in Montana, one in Nevada, and one in... Mississippi or Alabama; one of those states.

There was another one where I just decided to drive to Las Vegas and the middle of California rather than fly. I got remarkably sick on that trip, while I was in Vegas, and ended up infecting half of California.

And I'm pretty sure I did that more than once. Not the getting sick part, but the driving part. Like, the last time, I drove to Las Vegas and decided to follow US 60 on the way back. Oh yeah, that was the year I went to Nerd Camp in Colorado and proceeded to Vegas afterward. Also spent some extra time in Colorado on that trip, but somehow managed to find exactly 0 legal cannabis shops.

So let's see. More shit that happened to me in the 2010s. Oh yeah, I had a heart attack. No big deal. I spent a month on Maui. That was awesome, even though it happened to coincide with a time when I had some massive pain in my neck.

Maybe it wasn't actually a "lost" decade. Maybe it was a decade of decadence. A decade dance. Appropriate for a Waltz, I suppose. Beer was a constant. One of my reasons for traveling was to sample as many different beers from as many different places as possible. Did you know that Utah has some excellent breweries? You wouldn't expect it, but it does.

I can't help but think about what the next decade might bring. I have some plans, but life has a way of interfering with them. No point in speculating; if I'm alive to do so, I'll play the recordings here. Until then, here's some Leonard Cohen.

8 Like • Comment • View 10 comments

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