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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
Let ${z_1}$ and ${z_2}$ be two complex numbers with $\alpha $ and $\beta $ as their principal arguments such that $\alpha + \beta > \pi ,$ then principal $arg\,({z_1}\,{z_2})$ is given by
  • A
    $\alpha + \beta + \pi $
  • B
    $\alpha + \beta - \pi $
  • ✓
    $\alpha + \beta - 2\pi $
  • D
    $\alpha + \beta $
✓

Answer

Correct option: C.
$\alpha + \beta - 2\pi $
c
(c) We know that principal arguments of a complex number lie between $ - \pi $and $\pi ,$ but $\alpha + \beta $$ > \pi $,

therefore principal $arg\,({z_1}{z_2}) = arg\,{z_1} + arg\,{z_2} = \alpha + \beta $, is given by $\alpha + \beta - 2\pi $.

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