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 an hour 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.

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

February 25, 2019 at 12:31am

#953132

Wuv. Twue Wuv.

I've been hanging on to this one since before V-Day, and I'm finally to the point where I can read it without associating it with that disgusting holiday.

http://www.bbc.com/future/story/20190211-the-dark-side-of-believing-in-true-love...

Old-fashioned romantics might have the wrong idea about love. Strong beliefs in true love could be blinding you to both the good and bad in your partner, with sometimes toxic results.

Never thought the BBC would jump on the "You're Doing It Wrong" bandwagon, but I suppose that's spilled over into everything now.

Psychologists have found two scales that influence how we start and maintain relationships.

One measures how much importance we put onto first impressions and early signs of compatibility, while the other measures how likely we are to work through problems in relationships. They are called implicit theories of relationships (because we don’t often talk about them). We might intuitively think of ourselves as more or less likely to believe in true love – but this is not something that we openly discuss with others or are conscious of when we start new relationships.

Right, and I'm sure that these were verified in scientific tests and then replicated by other researchers.

Regardless, I skimmed over the quizzes. But they might be useful to someone.

Particularly in the early stages of a relationship the presence of an issue can precipitate a break-up, as the destiny believer realises that their “perfect” soulmate is fallible. The destiny believer may argue that their partner “never really understood me” or that a small fault is “evidence that we’re not really compatible.” This is the case even if the couple are relatively well matched, Franiuk has found.

This is also an abominably common plot device in romantic comedies. Or at least the few I've seen.

They say the course of true love never did run smooth – but a greater awareness of our own romantic tendencies might just help us navigate those bumps and turns along the way.

"They" don't "say" that - Shakespeare said that, and in a play that was even more a satire on love and destiny than the infamous Romeo and Juliet was. It's a sad day indeed when a British publication fucks up a Bard quote...

3 Like • Comment • View 2 comments

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