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4-1.Complex numbers
hard
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 $
C
$\alpha + \beta - 2\pi $
D
$\alpha + \beta $
Solution
(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 $.
Standard 11
Mathematics
