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 8 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 10 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.

July 13, 2020 at 12:01am

#988003

Summer Ale

My favorite summer activity is the same as my favorite fall, winter, and spring activity.

PROMPT July 13th

Write about your favorite summer activity.

The only difference is a) where it happens (indoors or outdoors) and b) what kind of beer.

When I was a kid, in the summers I'd relax after a long mammoth hunt by swimming in the bay behind our house. Okay, no, I'm not really that old, but once I start a running joke, I don't know when to quit.

It gets hot in Virginia in the summer. Hot and humid. My dad didn't believe in air conditioning, so during the hottest parts of the summer, I'd cool off in the calm waters. I'd see weekenders out in their sailboats and cabin cruisers, venturing sometimes to the marina next door. We had a garden, and back then I didn't kill plants just by looking at them like I do now, so I'd work in the garden or the field until I just couldn't deal anymore, and jump in the drink.

My feet got covered in crab pinch welts. Curse those arthropod demons.

I don't swim anymore. I don't live next to the water these days, and boating doesn't appeal to me except as a guest on someone else's craft. Too much work. And there's no way I'm going to deal with all the crowds, kids and germs at a public swimming pool.

When I was married, we'd go to the beach in September, when it's still warm but the place is nearly empty, other peoples' kids at school. Never did see the attraction of sitting on the beach doing nothing. If I'm going to do nothing, I might as well do it in the shade or, better yet, in air conditioning. It doesn't help that my skin is as pale as a white rabbit covered in snow, and I utterly despise putting on sunscreen.

I'm not much for separating beer by season; I'll happily drink a stout in summer and a wit in winter. But the yearly cycle of beer styles does have some effect in that the lighter beers tend to be more available in the summer.

My favorite beer season, if not my favorite weather season, is fall. Then, the Oktoberfest lagers and pumpkin ales come out, and most of them are just not available at other times of year. In the winter you have your stouts and spiced beers, and in the spring... well, there's not much special going on in the beer world in spring, except that it's the time when breweries tend to open their outdoor seating after a long winter, and you can sit there enjoying a wide variety in the open air.

But in the summer, a nice pale brew can be refreshing. While I'm not a big fan of IPAs, there are wheat beers, lagers, whites, and other brews of relatively low ABV that suit the season. But again, if I feel like drinking a heavy, high-octane stout in the 90 degree heat? I'll drink one.

So that's my favorite summer activity: drinking beer. Doesn't matter where I am: beach, mountains, suburbs, home... these days, of course, it's mostly at home.

When I can do it again -- if I can do it again -- I'm going to do a summer road trip, visit breweries in exotic locales like Michigan, Texas, or the West Coast. Maybe even Canada if they ever decide to let us barbarians back in. Most of my road trips have been fall or winter, which always runs the risk of accursed snow.

Just as long as I stay out of the direct rays of the blasted daystar and there's a beer at the end of the day.

9 Like • Comment • View 8 comments

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