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## Main Question or Discussion Point

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

Basically, he explains in this book that e was chosen as a base in the general form w = b

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.

^{[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 = e^{z}, 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 = b

^{z}because it reduces the ambiguity of b^{z}.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.