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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Turkey DrumStik

about 7 hours ago
In response to "Barley There"

And approximately 15 seconds later, someone's going to screech about genetically engineered crops.

That would be me...screeching for more genetically engineered crops.

Write_Mikey_Write!

Nov 14, 2024 at 2:04pm
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

Nov 14, 2024 at 12:10pm
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.

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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').

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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

November 4, 2018 at 12:33am

#944843

Past Times

The noughties were a strange time for me.

I have a hard time letting go of the past. I've said it before, but all the "living for the present" rhetoric doesn't ring true for me; by the time you register something as being in the present, it's already in the past.

"Noughties" was my coinage, by the way. No one else seems to know what to call the first decade of the 21st century. Nothing else fits, so "noughties" it is - any year of the format 200* gets shortened to 0* and is, therefore, the noughties. It never caught on, partly, I think, because I'm utter crap at self-promotion. (Yes, I know that decades begin at the year ending with 1 and end 10 years later at the end of the year ending with 0, but popular usage works otherwise, so I'm sticking with that.)

But I digress. By 2004, my mother had been gone for five years, and my father was effectively gone, though it would be another four years before his body joined his mind. I was married, but otherwise adrift - I'd quit my job of 15 years and gone to work for someone else in the same field, but the change was still a difficult thing for me.

Having always had a thing for writing, it was in that year - 2004 - that I joined Writing.com. I don't know how it is for other people, but for me, whenever I told someone that I wanted to write and get published, they'd look at me like I was an alien. Or maybe they just felt pity for me, because getting published might as well be winning the lottery. Or they just figured there's no way an engineer can also be a fiction writer, possibly for reasons I touched on in my entry about knowledge and creativity a few days ago.

Thing is, I didn't have that problem here. Mostly everyone else on this site is in a similar situation - loves to write, isn't exactly Stephen King.

I learned stuff about writing. It's a mad, complicated process that it's impossible to get perfect at. As with cooking, there's always something more to learn, something else to incorporate. But that's not why I stuck around.

I stuck around because I made friends.

I'm not going to list them here, because, inevitably, I'll miss someone and they'll feel left out. But you know who you are, especially if I've met you in person. Hell, I've traveled all over the country and beyond meeting WDC people. There are experiences I'd probably never have had without the people I've met here, including sampling wines in California, seeing the final Space Shuttle launch (sort of), and staying in a house in England that's older than my country.

And I'm happy to add new experiences and people to the list, especially if you buy me beer.

9 Like • Comment • View 5 comments

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