I'm reading a book called The Road to Reality by Roger Penrose, and I'm on the chapter for complex logarithms. What I don't understand is how the identity e[tex]\theta i[/tex] = cos [tex]\theta[/tex] + i sin [tex]\theta[/tex] is found through the use of complex logarithms. I also don't understand how if w = ez, z = log r + i[tex]\theta[/tex] if w is in [r, [tex]\theta[/tex]] form. Basically, he explains in this book that e was chosen as a base in the general form w = bz because it reduces the ambiguity of bz. I guess I'm just not seeing how the complex logarithm comes into play for the Euler formula being developed. EDIT: Sorry about the format of the post, I was just trying latex. I hope someone can clear this up for me, because I feel it's something obvious I'm not understanding.