A) \[{{\tan }^{-1}}\frac{5}{\sqrt{3}}\]
B) \[{{\tan }^{-1}}\left( -\,\frac{5}{\sqrt{3}} \right)\]
C) \[{{\tan }^{-1}}\frac{\sqrt{3}}{5}\]
D) \[{{\tan }^{-1}}\left( -\frac{\sqrt{3}}{5} \right)\]
Correct Answer: D
Solution :
Let \[z=5-\sqrt{3}\,i\] Þ \[r(\cos \theta +i\sin \theta )=5-\sqrt{3}\,i\] Þ \[r\cos \theta =5\]and \[r\sin \theta =-\sqrt{3}\] \[\therefore \] \[\tan \theta =-\frac{\sqrt{3}}{5}\Rightarrow \theta ={{\tan }^{-1}}\left( -\frac{\sqrt{3}}{5} \right)\]
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