by the way, I kind of completely proved this formula, the sin(ix) and cos(ix) part and I had help for proving sin(a+b) = sin(a)cos(b)+cos(a)sin(b) from wikipedia (just for the initial geometric figures for the proof) and I derived this formula too. ANYWAYS, you may have noticed that I have not been particularly active recently. this is in part because I have been very busy this summer with travels, and I also have been very interested in math, including calculus and complex analysis. And I also have some school work for high school I have to do. But, this is a project for my interest in mathematics. This is the graph of the sine function of a complex variable z = x+iy (with some zoom). the end value has been converted to polar form (angle and magnitude) so that I can show it as color and brightness. lighter is greater value, and darker is lower value. and the formula is in the project. its math update: re-sharing because I made an error where I forgot to divide by two when calculating the hyperbolic functions. resharing.
