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 2 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!

a day 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

a day 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.

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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

February 6, 2019 at 12:08am

#951279

New York State of Mind

Lyn's a Witchy Woman

: Yup, we're going to meet the famous Norb. It's only going to cost 750 gps for your phenomenal experience.

We're taking a limo ride so you'll get to see some of New York's gorgeous landscapes. You might even sneak in some shut eye after the Big Apple.

There's five cool things to see in Cortland before we hook up with Norb.

https://www.tripadvisor.com/Attractions-g47543-Activities-Cortland_Finger_Lakes_...

I spoke with the owner of Pontillio's and he's agreed to close the joint so we can have a private party with Fivesixer Here's your chance to ask questions or maybe grab his autograph, You do know he's published now. Hope you're in the mood for pizza.

https://www.tripadvisor.com/Restaurant_Review-g47543-d458524-Reviews-Pontillo_s_...

I'm always in the mood for pizza, especially the ones they sell in New York, which are the One True Pizza. Yes, even Italy can't do pizza as well as New York.

Cortland looks like a small town, but it boasts at least one brewery:

https://www.cortlandbeer.com/

As a bonus, it's also a distillery, so once again I have to break from the agenda.

My main reason for traveling around the US so much is to sample the wide range of fermented and distilled beverages available in every state. Naturally, some states are graced with more than others, because laws vary. In Kentucky, for example, there are bourbon distillers that are located in dry counties - figure that one out, if you can.

There are over 6,000 breweries in the US, and I don't think I've visited even 1/10 of them. Also, the nature of the business makes it so that, on average, every week we lose one and gain two. My favorite are the brewpubs - places where you can sit down, sample the beer, and also enjoy the food. Fortunately, this is also the largest category of brewery, these days.

It's a Sisyphean task to try to hit all of them, but someone has to try. This is made even more difficult by the excellent purveyors of fine beverages located near me in central Virginia - why travel when I have what I need right here? Well... I travel anyway.

But my love for beer is surpassed only by my love for pizza, so I'm happy to check out a new (to me) pizza place, as well, along with folks like 🌻 thankful pwheeler nano

and Prosperous Snow celebrating

5 Like • Comment • View 6 comments

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