Question

The argument of the complex number $\frac{13-5i}{4-9i}$ is

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{5}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (B)

The argument of $z$ is ${\tan }^{-1}\frac{y}{x}$.
Let $z=\frac{13-5i}{4-9i}\times \frac{4+9i}{4+9i}$
$=\frac{52+117i-20i-45i^2}{(4{)}^2-(9i{)}^2}$
$=\frac{52+97i+45}{16+81}$
$=\frac{97+97i}{97}$
$\Rightarrow$ arg (z) $={\tan }^{-1}\left(\frac{1}{1}\right)$
$=\frac{\pi }{4}$