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.
Having drunk soda on both sides of the Atlantic, I have to say that Mountain Dew with HFCS in America tastes a lot better than the 'same' drink made with sugar here in the UK. The experience is smoother and so is the taste.
Annette- I appreciate the recommendations, but I canceled Netflix when the choice was to put up with ads for a lower price or pay a shitload of money. If it were free with ads, I'd manage like I did in the days of broadcast TV, but I flat-out refuse to both pay money and watch commercials, which is why I never had cable TV.
The price for the ad-free experience also went up to the point where it wasn't worth it with the amount I watched.
I refer to my three languages as three different brains. In France, I activate my French brain. Which made for some funny turns of phrase when I was speaking to my son in English with English words, but in French syntax.
Netflix has some really good multilingual TV series. I recommend
I use translation tools all the time... and subtitles on youtube.
My French pronunciation is okay because I learned it as a child; my Spanish is okay because I practiced it. I slip into both with one key exception. French is easier when I'm depressed and Spanish can draw me out of depression.
Speaking multiple languages has also been linked to delayed onset of dementia symptoms.
Yes, I saw that you repeated that. It bears repeating.
Speaking multiple languages has also been linked to delayed onset of dementia symptoms. Or so I hope.
Well as someone who only hears out if one ear..I prefer to be able to hear completely any sound or noise or whatever. There are sounds you never would miss until you can't hear them anymore.
Anyway each to their own..I also prefer silence at times too.
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