Answer to Question #116083 in Complex Analysis for Jflows

Question

9.The principal value of the argument of (1+ ˆš3)(1−i) is____
\\(-5\\fra{\\pi}{12}\\)
\\(\\fra{5\\pi}{12}\\)
\\(\\fra{-\\pi}{12}\\)
\\(\\fra{\\pi}{12}\\)

Answer 1

$$Arg((1+i\sqrt{3})(1-i))=Arg(1+i\sqrt{3})+Arg(1-i)=$$

$$={\pi\over 3}+(-{\pi\over 4})={\pi\over 12}$$