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:

Write_Mikey_Write!

about 22 hours ago
In response to "Global Domination"

A little girl wearing a Hello Kitty shirt in Middle-of-Nowhere, Siberia will certainly make you wonder how it got there. My grandson has a souvenir t-shirt with a Terex 33-19 "Titan" on it. When it was built in 1973, the Titan was the largest, highest payload capacity truck ever built, a title it held for 25 years. The thing is, the truck on that t-shirt is on display in Sparwood, BC, Canada - over 1000 miles from here, and his mom got the shirt at a local thrift store. Makes me wonder.

Oh, yeah - I thought 'Schrödinger's Hello Kitty' was funny, too.

1 Like

Adherennium Plotting something

about 24 hours ago
In response to "Global Domination"

For whatever warped reason, 'Schrödinger's Hello Kitty' has tickled my funny bone.

3 Like

Brandiwyn🎶

Nov 12, 2024 at 10:50am
In response to "Blond Man's Bluff"

That's interesting about the two spellings of blonde. I always thought blonde referred to the person and blond referred to the hair. But I never bothered to look it up, So you've catered to my lazy today.

3 Like

Kåre เลียม Enga

Nov 9, 2024 at 1:02pm
In response to "It Was a Dark and Starry Night"

Ah... but why did he see those swirls when many of us don't? A totally different discussion... out of thin air... which is a frozen fog today when I gaze out the window.

Humans have great skills of observation; some of us extraordinary skills. Is The Scream depictive or evocative? 😱

Turkey DrumStik

Nov 9, 2024 at 11:04am
In response to "It Was a Dark and Starry Night"

Frankly, I'm more surprised to see reasonably good reporting from CNN. I'd given up on their ability to rein in their tendency toward loaded speech.

2 Like

JayNaNoOhNo

Nov 8, 2024 at 12:00pm
In response to "Bungalow Bash"

For the love of God, what did I just read? That is by far the worst use case of a bungalow I've ever seen, and a fundamental misunderstanding of the value of front porches—and the size of bungalows.

Was this his point? Nope, I know what his point was. For a guy so worried about presentation, he certainly undercut his own arguement.

1 Like

Turkey DrumStik

Nov 8, 2024 at 9:47am
In response to "Bungalow Bash"

"People don't change their minds on the internet. They usually do that in books, battlefields, or not at all.

Yeah, that's a little bleak."

Bleak and also inaccurate.

1 Like

Kåre เลียม Enga

Nov 7, 2024 at 10:19pm
In response to "Past and Future Intents"

I must live in the present. In the past I daydreamed a lot... probably to escape the bruises of reality; however, I need to be more aware crossing streets or even how I get out of bed (no rapid movements without thinking of consequences).

I can envision a future more peaceful than the present because this time-and-place isn't the only "present" that's ever existed, and I do try to see the larger view (emphasis on 'try').

1 Like

Lilli 🧿 ☕

Nov 7, 2024 at 10:58am
In response to "Past and Future Intents"

If the aforementioned exercises don't help; there's still liquor.

3 Like

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

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.

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