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:

Writer_Mike

32 minutes ago
In response to "Paris, I Guess"

Elisa: Middle Aged Stik

- I thought it very interesting, to say nothing of extraordinarily coincidental, that your video mentions a lock-adorned bridge in Paris. I just finished reading Spymaster by Brad Thor, in which the Russian mastermind takes strolls from Kaliningrad's mainland to Kant Island. The bridge he uses is also festooned with locks placed by couples declaring their undying love for one another.

QPdoll

about 17 hours ago
In response to "Landmarks"

I hope you're enjoying every minute in France! What an opportunity.

2 Like

Wordsmitty ✍️

about 20 hours ago
In response to "Landmarks"

Hey! Why are the signs at that Mac's in English if you're in France?

With all that walking, I hope you stayed hydrated.

2 Like

Annette in France

a day ago
In response to "Paris, I Guess"

Bienvenue en France.

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

last one today:https://parisjetaime.com/eng/event/olivier-giraud-how-to-become-a-parisian-in-one-ho ur-e047

1 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Could not resist sending the link: https://www.atlasobscura.com/things-to-do/paris-france

1 Like

Elisa: Middle Aged Stik

a day ago
In response to "Paris, I Guess"

Your remarks on Paris looking like many cities reminds me of this video (which I promise is short). It's a sassy look at Paris, and I'm here for it.

https://youtu.be/ByUPFYxy5vw?si=lT57RpTDntAhFdBs

2 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

if you have two hours to spare tomorrow? A beer bike tour in Paris. Check it out, still available. https://parisbeerbike.com/

3 Like

WakeUpAndLive️~Happiness

a day ago
In response to "Paris, I Guess"

Je suis sure, vous avez aimez la ville!!!!

2 Like

Aiva Raine

Sep 20, 2024 at 10:13pm
In response to "Get Baked"

FYI- basting them with olive oil before placing them directly on the oven rack- NO tinfoil- will allow the skin to crisp up a little as well and add a nice flavor to the skin. Recommend Idaho baking potatoes as well for best results.

July 3, 2023 at 2:36am

#1052054

Another Fine Mess

Finally, some vindication.

What If You Just Didn’t Clean That Up?

Good news: America has officially entered its messy-house era.

Like I needed to wait for permission.

Then, this past week, Marie Kondo herself admitted her house is a mess now that she has kids, a statement that was received like a divine pardon by mothers the world over.

I guess the mess finally sparked joy.

I’ve been waiting for this change for a long time, not because I love a mess, but because I have always had conflicted feelings about the moral supremacy of cleanliness.

I want to make a distinction here that the article kind of glosses over, at least at first: there's a difference between mess and clutter. Mess, to me, is not cleaning up your cat's puke, having pizza boxes lying around, or leaving dirty dishes in the sink. There are reasons to deal with messes that have nothing to do with morality, such as minimizing bug infestations. Clutter, on the other hand, is just stuff being organized in non-traditional ways.

The problem comes in when the clutter gets in the way of cleaning up the mess.

...mess is a sign of minds engaged in more important pursuits than tidying up.

And that used to be my excuse.

We need our ideas about cleanliness to catch up with reality, because they are stuck in the mid-20th century, when most women didn’t work outside the home.

We also need to stop using staged real-estate ads as an ideal.

Women were responsible for housekeeping for thousands of years, up until just a few decades ago.

[citation needed]

For two-income families who can’t afford a full-time housekeeper, maybe caring less is where the solution lies.

There is, indeed, a great deal of freedom when you finally stop giving a shit.

I know there are some readers who bristle at this because it smacks of lowering one’s standards to accommodate masculine laziness.

The messiest people I have ever known, not excluding myself, were my first wife, and a woman I dated for a while in the 90s. I freely admit that I'm lazy, but compared to them, I'm a cleanaholic.

Valid point!

No, it's not, you sexist sow. The neatest person I know was a guy who lived in my spare room for a couple of years.

Cleanliness has historically been about well-being, peace, and, to a lesser extent, health. But “clean” and “dirty” are also categories dreamed up by social groups.

I'll also point out that there's an element of privilege involved.

My parents came of age during the Great Depression. That period, at least in the US, left scars on the people who lived through it. They hated to throw anything away, on the grounds that it might come in handy one day. It's a scarcity mindset. If you keep throwing your stuff out, then you have to keep buying more stuff to replace it later on. This only helps merchants, and I'm pretty sure that's why they keep promoting minimalism: it's basically a marketing ploy.

Best to not buy all that shit in the first place, but obviously, the marketers don't go in that direction.

Meanwhile, product marketing has convinced us that we have to clean obsessively for our health. I can report from extensive first-hand experience that things can get quite filthy before people are actually getting sick.

And that's the other marketing push: buy these cleaning products to improve your life!

In conclusion, while I have some issues with the way the article is presented (not just the stereotyped gender roles, but way too many mentions of DikDok), I appreciate that someone else understands the value of not living in a perfectly curated space. It's one less thing to be neurotic about in a society that tries to make us neurotic about everything.

5 Like • Comment • View 5 comments

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