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 13 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 15 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.

May 17, 2020 at 12:02am

#983761

Reverse Road Trip

I do miss road trips.

PROMPT May 17th

Write about a fictional road trip where you meet up with your fellow competitors from the 30DBC! Who do you visit first? Do you bring any gifts? Tell us about the crazy blogger shenanigans you all get up to!

I have, indeed, visited several people from WDC while on the road, coast to coast in the US and even in exotic countries (the UK). Maybe someday I'll be able to do that again. Meanwhile, even thinking about it pisses me off. It pisses me off enough to get really drunk.

So for this fictional road trip, for once, I'm not going to be doing the driving. Y'all are coming to me.

You can bring beer, or wine, or scotch, or tequila, or, well, any booze of choice. I suppose if you're opposed to the very idea of alcohol (and somehow want to visit anyway), I will graciously accept chocolate. I promise I won't try to shame you into drinking.

Don't bring your underage kids, or dogs. Cats are acceptable. So are hamsters, but here, sign this waiver. I have cats.

I have Movie Night planned. Don't worry; I'll spring for the microwave popcorn. While the temptation is there to share my all-time favorite movies, they don't exactly have crowd appeal. Is Cats out on streaming yet? No? What's that? It'll always be "No?" Oh, very well. How about the Complete Works of Zack Snyder? Hey, where's everybody going?

Okay, okay, then comedy it is. Normally I'd propose Monty Python, but the plague scene in Holy Grail might hit a little too close to home. So we're going on a Gene Wilder kick. Wonka first to warm up, and then the Holy Trinity of Young Frankenstein, Blazing Saddles, and The Producers.

By the time it's over, you'll all be crashed in the living room and it won't matter that there's only one guest bedroom.

I'll even cook breakfast the next morning, assuming someone else goes shopping for eggs, biscuits, bacon, pancake mix, and OJ. I'm not leaving the house.

And don't worry, I won't make you schlep any leftover booze back with you. I'll heroically volunteer to hold onto that.

Seriously, though, I miss road trips.

6 Like • Comment • View 5 comments

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