A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{5}\]
D) \[\frac{\pi }{6}\]
Correct Answer: B
Solution :
Key Idea The argument of \[z\] is\[{{\tan }^{-1}}\frac{y}{x}\]. Let \[z=\frac{13-5i}{4-9i}\frac{4+9i}{4+9i}\] \[=\frac{52+117i-20i-45{{i}^{2}}}{{{(4)}^{2}}-{{(9i)}^{2}}}\] \[=\frac{532+97i+45}{16+81}\] \[=\frac{97+97i}{97}\] \[\Rightarrow \] \[z=1+i\] \[\therefore \]\[\arg (z)={{\tan }^{-1}}\left( \frac{1}{1} \right)=\frac{\pi }{4}\].
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