Property of  Log(z).  We know that , what about Log(z)?

Demonstration of Property of  Log(z).

Since the Mathematica function  Log[z]  is the principal value of the logarithm, we will investigate the relationship for  .  

Remark. The above formulas are for  Log[z]  and not  log(z).  What do you think about those pesky ArcTan's ? They are functions of two variables and evaluate properly throughout the complex plane to find  Arg[z].

      

(c) 2006 John H. Mathews, Russell W. Howell