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