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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is
  • A
    $\frac{\pi }{3}$
  • ✓
    $\frac{\pi }{4}$
  • C
    $\frac{\pi }{5}$
  • D
    $\frac{\pi }{6}$
✓

Answer

Correct option: B.
$\frac{\pi }{4}$
b
(b)$arg\left( {\frac{{13 - 5i}}{{4 - 9i}}} \right) = arg(13 - 5i) - arg(4 - 9i)$
$ = - {\tan ^{ - 1}}\left( {\frac{5}{{13}}} \right) + {\tan ^{ - 1}}\frac{9}{4} = \frac{\pi }{4}$

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