Correct Answer - Option 1 : 0
Explanation:
The argument of a complex number z = x + iy
\(\arg z = {\tan ^{ - 1}}\left( {\frac{y}{x}} \right)\)
\({Z_1} = 5 + \left( {5\sqrt 3 } \right)i,{Z_2} = \frac{2}{{\surd 3}} + 2i\)
Then \(\arg{Z_1} = {\tan ^{ - 1}}\left( {\frac{{5\sqrt 3 }}{5}} \right) = 60^\circ\)
And \(\arg{Z_2} = {\tan ^{ - 1}}\left( {\frac{2}{{\frac{2}{{\sqrt 3 }}}}} \right) = 60^\circ\)
So, \(\arg \left( {\frac{{{Z_1}}}{{{Z_2}}}} \right) = \arg \left( {{Z_1}} \right) - {\rm{arg}}\left( {{Z_2}} \right)\)
\(\arg \left( {\frac{{{Z_1}}}{{{Z_2}}}} \right) \) = 60° - 60° = 0