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!

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

Turkey DrumStik

Nov 6, 2024 at 10:22am
In response to "Lo!"

Not gonna lie I need the holiday season chatter.

August 31, 2019 at 12:19am

#965280

What About Money?

For this, my final August post (I'm going back to the 30DBC tomorrow), I'm going to take my chances with Psychology Today.

https://www.psychologytoday.com/us/blog/think-act-be/201907/what-your-relationsh...

Before I delve into the clickbaity part, I would like to point out the menu bar on top of the webpage:

"Find a Therapist." "Get Help." You know, just in case you were wondering if the universe was trying to tell you something.

Actual article:

What Your Relationship with Money Reveals About You
...and why romantic partners often fight over finances

More like: What your relationship with money reveals about your relationship with money. Come the hell on.

Money is a complicated topic. Most of us tend to feel uncomfortable talking about it, and might even prefer to reveal aspects of our sex lives than to divulge our income.

"Yeah, I like to go to S&M clubs dressed as a pink rabbit, get chased by someone in a fox suit until I can't breathe anymore, then let them have their way with me until I pass out. What's that? How much money do I make? That's personal!"

Do you feel like there’s never enough money, and always too many expenses? Does it pain you to spend money? You may have a scarcity mindset, as described by Steven Covey in his bestselling book The Seven Habits of Highly Effective People.

The book The Seven Habits of Highly Defective People is harder to find, but probably more useful.

And without realizing it, those early experience “can haunt you 20 years later,” said Honda. For example, maybe your parents couldn’t afford the fashions that the other kids were wearing, so you developed a feeling of inadequacy.

My parents could damn well afford them, but I ended up with discount rack seconds anyway, because they were cheap fuckers. You know what, though? It built character, and I don't obsess over what I wear now.

For example, if we dreamed of getting a nice toy but couldn’t afford it, we might come to believe that the things we really want in life will always be out of reach.

The trick to that is to make sure to only want things that are in reach. Life is easier, simpler, more rewarding, less stressful, and happier that way.

As Honda noted, it’s often no accident that people with opposing views of money end up together. “For a saver, a spender looks so attractive,” he said, “because they know how to enjoy life. And a spender is attracted to a saver because they offer security.” And while these aspects may have drawn the couple together, after a while, the same tendencies can become sources of irritation.

No, don't think of that as sources of irritation. Think instead of the great material you're giving comedy writers!

1 Like • Comment • View 4 comments

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