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 2 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 4 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.

August 17, 2021 at 12:01am

#1015729

Fence

Okay, so today's article is about one particular life decision, but it seems to me -- someone who is not well-versed in psychology -- to have other applications. So here it is.

I help people decide if they want to have kids. Here’s my advice.
A parenthood clarity therapist explains how she helps fence sitters make one of the most important decisions of their lives.

I made that particular decision long ago, though I understand that the pressures and consequences tend to be different for women. But once I realized I did have the power to make the decision, it was an easy one. The trick was avoiding the societal pressure to conform to a particular life script.

I’m a therapist who has dedicated my life to helping people figure out if they want to have children. I’ve been doing this for 30 years and have seen more clients than I can count of all stripes — men, women, single, married, and partnered people. People just out of a relationship and people just starting a relationship. People from ages 28 to 59. Our goal is to help people make possibly the biggest decision of their lives: whether or not they want to become a parent.

Apparently, questioning that life script is more common than I thought.

Many assume that a time will come for each of us, at which point we’ll “just know.” Even though that is the case for some, it’s a myth to think it’s that way for everyone.

Yeah, I think I can pinpoint the moment when most people "just know." By then, it's too late, and you're committed.

From desperation, they have to make a decision. Fear instead of desire runs the show. Operating on fear is a lonely, excruciating process that leaves many immobilized. But when a decision is made from a place of desire, joy, or clarity, the experience is quite different.

That's the key bit that I think might be more generalized.

The article goes into some shrink-rap type exercises, which, to be honest, I skimmed.

Now, I don't want people to get the idea that I'm proselytizing my own point of view here. Personally, I think the world would be best off if everyone who wanted children could have them, and everyone who didn't want them, didn't. From my perspective, if you're going to worry about regrets one way or the other, it's better to regret not having kids than to regret having them. I mean, consider what that attitude could do to a child, even if you never say it out loud. (Of course, it's best to have no regrets, either way.) But often, parents press their decision on others: "It's so rewarding! You'd be missing out on such joy! You'll never know what real love is!" All I'd say to anyone on the fence is: don't listen to those words; look at what their lives are like and decide if that's really what you want. And pay particular attention to any sentence that begins "I love my children, but..."

But anyway, like I said, that's not the only major decision people will make in life. For example, should I have beer tonight, or scotch? Or maybe both? Likely I'll decide it at random, because then I can blame the random number generator if things don't go as well as I hoped.

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