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

about 10 hours 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.

1 Like

QPdoll

a day ago
In response to "Landmarks"

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

2 Like

Wordsmitty ✍️

a day 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

Sep 21, 2024 at 7:34am
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

Sep 21, 2024 at 6:46am
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

Sep 21, 2024 at 6:16am
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.

February 26, 2023 at 9:21am

#1045558

Revisited: "Random Thoughts"

It's Throwback Sunday (maybe I should start doing these on a Thursday), and the random number generator gave me another one from 2009, mid-September: "Random Thoughts"

Sadly, this is mostly not my work. While I'm certainly not above quoting sections from an article I link to comment on, it isn't usually my style to just copy something whole-cloth, even if it is something that was circulating widely at the time. I don't know; I may have done it more in the distant past—I don't remember, which is one reason I do these retrospectives. But I don't do it much, if at all, these days. My blog is to emphasize my thoughts, not someone else's.

The entry does start out with me:

A friend of mine just discovered the wonders of email.

Again, this was 2009. I think I first got an email account in 1994, unless you count the one the university assigned to me as a student in the eighties.

This means that she's currently forwarding every bit of glurge and misinformation on to all of her hapless friends.

I'm at a loss to remember who this was. Probably she's all over Failbook and DikDok now.

I was just about to relegate her latest recirculated bit of "wisdom" to the compost pile when I accidentally looked at it.

And laughed.

What can I say? Wade through enough shit and eventually, you'll find a penny.

Re-reading these now, I don't think they're quite as funny. I won't paste all of them again here.

I wish Google Maps had an "Avoid Ghetto" routing option.

Probably racist, definitely classist.

I totally take back all those times I didn't want to nap when I was younger.

Inertia is a thing. If I'm awake, I want nothing more than to stay awake. If I'm asleep, I want nothing more than to stay asleep.

There is a great need for sarcasm font.

Comic Sans is the Official Sarcasm Font.

I would rather try to carry 10 plastic grocery bags in each hand than take 2 trips to bring my groceries in.

Wow, that one didn't age well.

Map Quest really needs to start their directions on #5. Pretty sure I know how to get out of my neighborhood.

Nor did that one.

Bad decisions make good stories

This one, however, is timeless.

Can we all just agree to ignore whatever comes after DVDs? I don't want to have to restart my collection.

Well, that didn't happen.

While watching the Olympics, I find myself cheering equally for China and USA . No, I am not of Chinese descent, but I am fairly certain that when Chinese athletes don't win, they are executed.

Eesh.

I hate when I just miss a call by the last ring (Hello? Hello? Darnit!), but when I immediately call back, it rings nine times and goes to voicemail. What'd you do after I didn't answer? Drop the phone and run away?

I have no idea what this means anymore.

As a driver I hate pedestrians, and as a pedestrian I hate drivers, but no matter what the mode of transportation, I always hate cyclists.

This hasn't stopped. It needs to. Desperately.

I think the freezer deserves a light as well.

I have a warped sense of time, but I'm pretty damn sure my current refrigerator is one I bought long before 2009. Its freezer features a lightbulb.

Well, that's enough of that. Some of the ones I didn't re-glurge-itate here are still legitimately funny, but these days, instead of being forwarded around in email, they'd all be pasted on top of an image of some sort. Because our attention spans really are SQUIRREL!

3 Like • Comment • View 3 comments

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