Originally posted by sonhouseHe used another way of writing i:
What is n in that equation?
And how does PI enter into this? interesting.
Also, what does exp mean? exponent? if so, what exponent?
Originally posted by AThousandYoungIt's not part of the defiition of i, but it's an extremely useful general result:
i is part of the definition of i? That doesn't make sense.
Originally posted by mtthwI'm getting PI i'd thinking about this:
It's not part of the defiition of i, but it's an extremely useful general result:
cos(theta) + i sin(theta) = e^(i theta)
He's using the case where theta = PI/2. Then the left-hand side is equal to i.q
Originally posted by PalynkaOr almost any serious applied mathematics. It crops up in wave theory, quantum mechanics, fluid dynamics, instability calculations...
Yep, someone that needs to deal with dynamic optimization should be familiar with it. It's called de Moivre's theorem.
Originally posted by mtthwNice. Thanks for that. I Goog'd De Moivre and found this neat wiki:
Or almost any serious applied mathematics. It crops up in wave theory, quantum mechanics, fluid dynamics, instability calculations...
Originally posted by sonhouseI love the fact that -e^(pi.i)=1. (also shown by de Moivre's formula)
Nice. Thanks for that. I Goog'd De Moivre and found this neat wiki:
This piece goes into it in some detail.
BTW, my present read is 'The Riemann Hypothesis"
by Karl Sabbagh. Anyone read this? Great read if you are into maths.
I think my next maths book will be 'the joy of i'. I think there is a book with something like that title.
Originally posted by FabianFnasI didnt know that!
Calculating with i ( as sqrt(-1) ) is only an extension of the real number system. What you can do with R you can do with C.
With the complex number system (C) you can calculate square root of any number (including complex numbers), not only positive numbers. You can calulate arcsin with any number (including complex numbers), not only ...[text shortened]... er one is that negative infinity is the same as positive infinity.
Complex numbers are fun!