Having hit the send button prematurely, John Randall wrote: > This is a special case of Euler's identity. I suggest > cos=:2&o. > sin=:1&o. > euler=:[EMAIL PROTECTED]@sin > euler 1p1 > 1 > euler ?0 > 1 > euler ?100 > 1 > euler j./ ? 0 0 > 1
What I had intended to add was that the general case of the formula gives the definition of exponentiation with imaginary exponents: the familiar identity gives the special case with argument pi. While this identity has some mystique, the real virtue is in extending exponentiation to the complex numbers through (surprisingly) the real trigonometric functions. Previously exponentials and trigonometric functions were thought of different species: now we regard them as essentially the same thing. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
