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:

Turkey DrumStik

about 9 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.

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

October 12, 2018 at 1:06am

#943253

Critical Miss

So this happened:

https://www.cbsnews.com/news/medieval-re-enactor-fatally-impales-self-with-his-l...

I've never been in the SCA or gone to any SCA events, but I tend to have friends with that proclivity. Hell, my ex-wife was part of that group. Add in the guy being from my state, and also close to my age, and I started to wonder if we had any friends in common.

Well, it turns out that one of my closest friends had known the deceased since 1991 - a lot longer than he's known me - and that Barclay had mentored him in several skills, including the holy art of brewing. I've reaped the benefits of this art a few times, so while I didn't know the guy myself, it's not farfetched to note that his life affected mine.

It's easy for "normal" people with "normal" hobbies to make fun of incidents like this, as if no one's ever died or been injured from football or street racing or whatever it is that normal people do. And they forget that this was a person with a family and people who cared about him - all that seems to matter to them was that he died doing something nerdy, so they can feel superior.

From what my friend has told me, Barclay was a multitalented individual with a great deal of knowledge and skill. Said knowledge and skill wasn't applied toward socially-acceptable activities such as chasing balls around or foreclosing on poor peoples' houses, so the bulk of society could safely dismiss him as one of those weirdos with padded swords and funny names. It doesn't help that I just got to the episode of Supernatural that features LARPing - really bad timing on my part. An escapist fantasy story mocks people who like to immerse themselves in escapist fantasies; it's almost as if the writers have no conception of irony.

Yes, I know that SCA != LARP, but the Venn diagram has a pretty big intersection.

Life is fleeting and any of us could kick it at any time. We should all be so lucky as to go out doing something that's aligned with our own truth. Preferably at 103 and not 53, though.

https://www.syfy.com/syfywire/man-dies-in-tragic-accident-in-medieval-recreation...

2 Like • Comment • View 7 comments

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