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 5 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

December 3, 2018 at 12:30am

#946746

When In Ramen...

They say it is important to have goals.

https://thetakeout.com/ramen-lord-perfect-bowl-of-ramen-mike-satinover-183012867...

There's focus, and then there's obsession. At least the guy admits to the obsession.

I just consider myself a ramen nerd. A wholly obsessed ramen nerd who loves to read academic articles about gluten development in noodle doughs, a nerd who’s spent way too much money on pasta machines that then broke through the rigor of making noodle dough, a nerd who—intentionally—owns six different types of bowls to suit various ramen styles.

"I don’t count the 99-cent noodle packets" - 99 cent? Where in the slippery hell are they charging that much for ramen? I shop at a moderately upscale grocery store and they're selling 6-packs for a buck and a half. That's 25 cents a pack for the math-challenged. Not that I eat much of that anymore, myself - my cardiologist would kill me if the sodium didn't do the job for him.

Dude must be shopping at Whole Foods.

Not that I never eat it. It's just too cheap and simple to pass up. And yes, I've eaten the similar Vietnamese-derived dish called pho.

Pho, as you probably already know, is pronounced more like "phuh." Which almost makes me wish I had what it took to start my own line of instant pho. I have good reasons for this.

I'd call it Pho King. The tagline would be "Awesome." So on every pack it'd say "Pho King Awesome." You buy the instant pho mix because you're Pho King lazy.

The basic package would be called the Pho Kit. Not feeling like standing in a Pho queue? Don't want to cook an elaborate meal? Pho Kit!

Being cheaply produced, though, it might make people sick - but then they can just Pho Cough.

But alas, it is not to be. Still, if I see it anywhere, I'll have this entry to point to and say, nope, I thought of it first; give me kickbacks.

Anyway. Ramen.

Learning to craft an A+ bowl of ramen is now my life goal. Maybe A+ is never possible, perfection is a impossible pursuit after all, but the path of getting closer and closer to that immaculate, flawless bowl intrigues me.

That's remarkably similar to something I've said about writing. How we can keep practicing, writing, trying different styles, and yet never be perfect. And yet, the reward is in the attempt.

I'm not used to thinking that way. This is new to me.

I've never stuck with one thing long enough to get really good at it. There's always something else to try, something shiny off in the corner of my vision. Again, this has its advantages, but seeing this description of someone doing a deep-dive into soup - so to speak - makes me think I might be missing out.

Meanwhile, now I'm hungry. Dammit. Wish I had a Pho Kit.

7 Like • Comment • View 4 comments

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