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:

Elycia Lee ☮

about 5 hours ago
In response to "There Is A Such Thing As Coincidence"

I loveeee the photo! You guys look good!

Coincidences are great! So happy you met!

2 Like

Wordsmitty ✍️

about 18 hours ago
In response to "Two Castles and a Cave"

That's definitely a wonderful picture that shows the whole story. When enlarged, it's a little fuzzy as if after quite a few bottles of wine.

1 Like

Annette in France

about 21 hours ago
In response to "Two Castles and a Cave"

After being in Tours for an afternoon/evening and only, my favorite part of my time there was to see you.
Old Tours with its medieval houses is charming to stroll through, but France has many charming old towns.

The most impressive cave system that I went to this vacation is under the Chateau de Brézé. It is where the Troglodytes lived. Their caves didn't only house people, they even had underground horse stables.

Interestingly, Chateau de Brézé is also a wine castle complete with an attached tasting room. Even the gift shop sells mostly wine along some postcards.

1 Like

Elisa: Middle Aged Stik

about 23 hours ago
In response to "Two Castles and a Cave"

Oddly enough, Tours is a sister city to Minneapolis. That still isn't enough of a reason for me to visit France, but it's still a nice bit of trivia.

2 Like

Kåre Enga in Montana

a day ago
In response to "There Is A Such Thing As Coincidence"

That's awesome. Enjoy your visit of the Loire.

TGV = tren à grande vitesse = HST. I only took it once, Paris > Luxembourg. Everything was a blur.

2 Like

Annette in France

a day ago
In response to "There Is A Such Thing As Coincidence"

That was a total coincidence. I didn't even plan to go to Tours at all. I was there because of the way I planned out a travel leg. To run into you on the other side of the Atlantic in a random town was pure luck.
It was fun to catch up with you.

2 Like

Brandiwyn🎶

a day ago
In response to "There Is A Such Thing As Coincidence"

Love it when stars align!

2 Like

Wordsmitty ✍️

Sep 24, 2024 at 5:15pm
In response to "All Out of Louvre"

I agree. You should always check the "Five Must Dos in ..." before you go, so you know what to avoid from crowds.

Smurfs are universal.

1 Like

Elisa: Middle Aged Stik

Sep 24, 2024 at 11:30am
In response to "All Out of Louvre"

That street art is definitely a step up.

1 Like

Annette in France

Sep 24, 2024 at 9:55am
In response to "All Out of Louvre"

I'm already out of Paris.

3 Like

March 14, 2020 at 12:02am

#978055

Poor You

Today, in Adventures in Book Promotion:

https://www.theguardian.com/money/2019/oct/08/online-poor-part-time-job

Online, no one knows you're poor
Shauna M Ahern used to make her living by writing a food blog. But when times got tough, she realised keeping up appearances can make you lose sight of life’s meaning

But what if life's meaning is keeping up appearances?

I am a James Beard award–winning gluten‑free cookbook author. And for nine months, I worked in our local grocery store for $15 an hour.

1) I'm only giving her a pass on the "gluten-free cookbook author" gig because she is apparently diagnosed with celiac.
2) $15 an hour? Stocking groceries? I'm not saying that's a lot of money, but it's above average for unskilled workers.

Online, no one knows you are poor. No one is posting photos of the basket of bills overflowing, some of the envelopes with urgent stamped on them. Very few people write about the choices they make out of fear of going bankrupt, like selling expensive camera lenses that feel less important than rent.

Maybe they should. One gets weary of seeing people's carefully curated photos and videos of their perfect lives. It's like watching those sitcoms set in the big city where no one seems to have a real job and yet they live in enormous apartments. Other people see that shit and, consciously or unconsciously, they wonder why they can't measure up. But hey, maybe if I buy the products advertised during the next break, I'll finally have a perfect life too!

And few of us want to admit that we are struggling with money, even though we live in a culture where the rich have grown astronomically rich and the rest of us have grown anxious about health insurance. As my friend Ashley Ford wrote online one day: “I’m trying to choose an insurance plan, but I’m pretty sure the only good insurance is wealth.”

No one wants to bitch about being poor, but also no one wants to brag about being rich. In general, no one talks about money. I don't think this is a good attitude, even though I'm cagey about it myself.

But yes, the only good insurance is wealth. In the US, anyway. I'm assuming this is US because even though it's a British rag, everything's in dollars and the author writes with the sort of humblebragging that one generally only finds in this country.

I never shared online the time that my husband Danny and I looked at our bank account and saw $85 left for the last week of the month.

Well, you have now.

Still, we were like most Americans – living paycheck to paycheck (almost eight out of 10 Americans, according to reputable studies) and unable to pay for an unexpected bill of more than $500 (nearly six out of 10 Americans). We were struggling. And we were terrified. I realized that the mindset of worrying that we might go broke was damaging us.

I can't be arsed to check those numbers, but if true, they're kinda horrific. And yeah, being broke, or close to it, damages one's mind. The crappy cheap food you have to buy if you're poor doesn't help with that.

I found out that working part‑time at the grocery store – three days a week – would give me health insurance for the entire family.

Tying health insurance to employment is good for employers. Not great for people who'd rather spend their time running a small business.

I noticed that the people who lived on the day‑old breads looked around furtively to make sure no one saw when they reached into the discount bin.

And we've established, somehow, the idea that there's some sort of moral failing, some shamefulness, in being poor. Like human worth is somehow tied to net worth. This is utter bullshit.

I learned that very few people make the highly styled dishes offered on Instagram.

YA THINK?

Over and over, I saw that what my fellow recipe developers and I hashed out to make ourselves relevant – Vegan treats for the whole family! How to use hempseed! – was not being made in most homes. It humbled me.

Good. Veganism is a product of privilege. And yet the same people who tout a "vegan lifestyle" tend to be the ones who spout "check your privilege!" It's a jarring contradiction.

Danny is the one working three days a week now, expediting in a restaurant, mostly for the connection with our community. I no longer earn any money online.

I'm not sure "earn" is the right verb. And again - you are making money online, shilling your book on the Guardian's website. Hey, there's no shame in that, either. I'd love to make money from writing; I think many people here would. But if this is the kind of writing style in the book, I'm not interested.

3 Like • Comment • View 1 comment

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