Thathabai Nowroji is at the Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli.

M Munisamy is at the Department of Mathematics, Kamaraj College, Thoothukudi.

Functions like log_e x, e^x, e^z and log_e z are defined and studied systematically. It is observed that e^z is the only complex analytic extension of the real analytic function e^x. It is also observed that the power (analyticity) of e^z is by choice and the beauty (its derivative is itself) of e^z is unexpected.

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Address for Correspondence
P Thathabai Nowroji
Department of Mathematics 
Manonmaniam Sundaranar University 
Tirunelveli 627012 
Tamil Nadu, India. 

M Muniasamy 
Department of Mathematics Kamaraj College 
Thoothukudi 628003 
Tamil Nadu, India..