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Tuesday, Jun. 25, 2024

8:57pm EDT

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Complex Numbers

by Robert Waltz

Rated: 18+ · Book · Personal · #1196512

Not for the faint of art.

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:

Anni Pon

about 11 hours ago
In response to "Can't Spell Success without Sucs"

I've never heard anyone say, "That guy is so successful, but he doesn't really make much money." Or anything similar. Sure, you can have a positive impact on the world without making lots of money, but people won't call it success.

1 Like

Annette

Jun 23, 2024 at 1:28pm
In response to "Revisited: "Experience""

This is how I coped:

1 Like

Elisa: Middle Aged Stik

Jun 23, 2024 at 9:51am
In response to "Revisited: "Experience""

Not gonna lie I kinda miss Zoom parties, at least for this community since people on WDC are so spread out. Meeting in person is pretty tricky and/or expensive. It's certainly more socializing than I've been doing regularly since, oh, 2022 or so.

As for server migration, well, I work in the IT world. I've been through that. And honestly, server migration is a bit nerve wracking, as some stuff can go missing. It's still more manageable than a complete redesign. Complete redesigns are awful. You can test in different environments that the public can't see till kingdom come, but things always go wrong when the public version is rolled out. A local grocery store recently redid their website, and the old site held thousands of recipes. When the new site was unveiled, none of those recipes made it over. I ended up reaching out on Messenger and was able to get a copy of a recipe I use somewhat often, but I'm kind of annoyed that the text recipes are currently MIA because somehow that data didn't transfer with the site rebuild. Absolute madness.

1 Like

Wordsmitty ✍️

Jun 22, 2024 at 5:56pm
In response to "Discomfort Zone"

Just so everyone is clear:

- There are credit cards and debit cards and even cash cards. They are treated differently by different places as some prefer debit and cash over credit (which usually chrages the merchant more).

- As Annette mentioned, using text and wi-fi is best and usually cheap or free included most US phone plans. However, 'data' outside N. America is not. If you want to wander streets and go hiking and check maps or GPS in Europe, make sure you have a data plan for Europe. That's where the thousands of dollar charges come in if you don't have that. Voice also is usually extra. So if you plan on a lot of talking, get a plan for that, too. (As I recall without an additional plan for Europe, standard charges were 25 or 50 cents for each text and and a dollar minute for voice.)

- On phones, you may have to turn on or unlock the ability to use European system as it communicates differently than the one used in the US. T-Mobile does have good info explanaing that and data plans once you find it on their site. I think there was a search to input your phone make & model to show you what will make it work outside N. America.

1 Like

Elisa: Middle Aged Stik

Jun 22, 2024 at 5:08pm
In response to "Discomfort Zone"

Funny thing is, everyone mentions day to day spending in cash, but I don't recall seeing a single person in the Netherlands use cash in the grocery store. I was in a couple different grocery stores and a convenience store outside normal tourist areas, and cards were preferred. Even in museums there were readers to get donations from cards instead of having boxes out to drop off cash donations. This may be less of a thing in smaller communities, but I do feel like some of the larger (non-tourist) communities are going cash free. The pandemic's legacy of contactless payments sure has been a weird one.

1 Like

Annette

Jun 22, 2024 at 4:51pm
In response to "Discomfort Zone"

I think that SIM card thing is over now. Check it out though. I didn't change my SIM card and I my bill was the exact same as always. I did only use texting and wi-fi though.

1 Like

Robert Waltz

Jun 22, 2024 at 4:46pm
In response to "Discomfort Zone"

Annette

, merci, tu as raison.

I have a pretty recent Samsung phone, and T-Mobile, but I seem to remember something about a different SIM card or activation or something. Easy enough to find out. I know there were horror stories for a while about people traveling and getting hit by surprise roaming fees in the thousands of dollars, so that would be something to avoid.

Thinking about going this autumn, because like you said, it's not summer. Also, hopefully fewer free-range tourist kids. One of the many great things about being me is that I have some flexibility, so I don't yet know exactly when.

1 Like

Annette

Jun 22, 2024 at 3:49pm
In response to "Discomfort Zone"

les bières en France sont mieux = meilleures (plural feminine beers)

The last time I went to France, I brought my Samsung Galaxy S8 and it worked perfectly for Google maps. I don't know what kind of phone you have, but if it's from 2018 or newer, you shouldn't have a problem with that.

I use T-Mobile and their plan includes sending text messages and using the internet (where available) without any upcharge. It's not a fancy plan, so I think it's a standard.

I don't know what kind of credit card you use, but Visa or MasterCard seem to be preferred to the others. I haven't had any problems using credit cards to rent cars or whatnot. I like to exchange some cash for small day to day purchases. It makes things easier and more fun too. Although I still think that the Euro looks like Monopoly money with its fake bridges on it.

When do you plan to go? I know, you said before your passport expires, but what does that mean?

Also, don't go in summer. It's too hot and they don't have air-conditioning. Anywhere!

1 Like

Robert Waltz

Jun 22, 2024 at 2:11pm
In response to "Discomfort Zone"

Thanks, Wordsmitty ✍️

, very helpful. Though I don't use ATMs at all, it shouldn't be a problem to set things up so I can do so. And yes, my CC specifically doesn't charge foreign transaction fees (they just don't do their usual cash-back with non-US transactions, which I can live with).

As for the local servers thing, as long as it's in French, I can manage. Or I can probably get a VPN for the phone.

Wordsmitty ✍️

Jun 22, 2024 at 2:03pm
In response to "Discomfort Zone"

Here's a few things that may help:

- Some places do require a PIN with the credit card like automated train ticket machines and such. Always good to make sure you verify your PIN before you leave.

- Some credit cards don't have foreign transaction fees to convert to US dollars. Check your credit card T&C or find a better cc.

- You probably know to never make the credit charge in US dollars if there's an option or they ask you. Make it in local currency.

- We get some local cash from an ATM before we leave the airport so we have it if needed. Also, some US banks and credit unions have a monthly allowance that reimburse ATM fees up to an amount each month (~$10 usually). Since it's cash, there's no conversion fee like charged with credit card transactions. Never use a credit card to get cash.

- Paying cash for little things along with knowing some of the language helps with the 'visitor' image.

- When connecting to the internet in Europe, you'll probably get local servers for Google and it will come up in the local language.

Have fun

1 Like

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