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If $z=\sqrt{20i-21}+\sqrt{20i+21}$,then possible value of arg(z) equals

(A) $\;\large\frac{\pi}{4}$

(B) $\;\large\frac{\pi}{2}$

(C) $\;\large\frac{3\pi}{8}$

(D) $\;\pi$

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1 Answer

$20i+21=(5+2i)^2$ and $20i-21=(2-5i)^2$
$\Rightarrow z=\pm (5+2i)\pm (2-5i)^2$
$\Rightarrow z=7(1+i),3(1-i),3(-1+i),7(-1-i)$
$\Rightarrow arg(z)=\large\frac{\pi}{4},-\frac{\pi}{4},\frac{3\pi}{4},\frac{-3\pi}{4}$
Hence (A) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
 

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