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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Show Recent Comments

10 Most Recent Blog Comments:

Write_Mikey_Write!

about 15 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 16 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.

April 3, 2020 at 12:12am

#980096

Ya Think?

I've been saying something like this for years.

https://theoutline.com/post/7142/be-yourself-is-terrible-advice?zd=2&zi=g32iywmn...

“Be yourself” is terrible advice
Take a better lesson from philosophy and me, a reformed loudmouth

Mostly, what I've said has been along the lines of, "Don't be yourself. Be what you want to be, and eventually that will be you." That and, "Be Batman."

Some great advice I once got was “Be less yourself.” This was in 2016, a couple of months after I left the Gawker website in part because I live-tweeted a meeting during which my boss hit his head on a lamp.

"Was that wrong? Should I not have done that?"

“Be yourself” is the kind of empty self-help mandate uttered by such disparate artists as Audioslave and Oprah; something that that is typically (and ironically) advised before coming into contact with strangers.

Coincidentally, I'm not a fan of either of those.

Luckily for everyone, I started going to therapy, and it was during one of my first few sessions that my kind therapist who gives me all of my article ideas told me that the consequences that came from what I thought was “being myself” could be avoided simply by not being what I thought was “being myself,” mostly because the former self was a huge asshole.

The single most constant fact of life, apart from death and taxes, is that people change. You can direct that change to improve yourself, or you can let it happen and who knows where that's going to go?

The first problem with it is that it is an impossible task: a holistic self does not exist; we are made of many selves that are revealed through endless experimentation and self-examination.

I didn't know I liked beer, for example, until I tried it. Until that point, I wasn't "a beer drinker."

The second problem is that today’s popular notion of the self mistakes feelings and desires for self-knowledge. Heidegger thought (extremely roughly) that knowledge of one’s authentic self could be found through the consideration of our own mortality: that feeling you might get after you have a near-death experience.

It is impossible to read anything attributed to Heidegger (or several other thinkers) without thinking of "Bruce's Philosophers Song" from Monty Python.

Hey, if it's stuck in my head, it needs to be stuck in yours as well.

Wittgenstein took a more social approach to self-discovery.

Him, too.

The author goes on to write some self-indulgent claptrap about having a dog.

Oh my god, is this me now? Am I a horrible, treacly, sentimental dog person?

Yes. Own that shit.

Heavens no.

You have learned nothing, grasshopper.

My friend John, who graciously explained a lot of Heidegger to me in the process of writing this article so if I’m wrong about any of it please blame him, said: “Ask yourself periodically, is this who I really wanna be?”

And she's still not owning her shit.

So there you have it: “Be yourself” is terrible advice. Especially if you are a jerk, but probably even if you are not.

Self-centered writing style aside, she makes some good points. It takes a bit of humility to recognize when you're wrong and other people are right. My own takeaway from this? Don't be so damn sure of yourself.

Of that, I'm certain.

3 Like • Comment • View 3 comments

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