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Complex no lying on angle bisector of $z_1$ and $z_2$ where $z_1=3+\sqrt 3i$ and $z_2=2\sqrt 3+6i$ is

$\begin{array}{1 1}(A)\;z=5+5i&(B)\;\;z=-4-4i\\(C)\;z=1&(D)\;\text{None of these}\end{array} $

1 Answer

arg $z_1=\tan^{-1}\large\frac{\sqrt 3}{3}$$=30^{\large\circ}$
arg $z_2=\tan^{-1}\large\frac{6}{2\sqrt 3}$$=60^{\large\circ}$
Angle bisectors arg =$45^{\large\circ}$
$\Rightarrow arg(z)=45^{\large\circ}$
Clearly option (A) satisfies.
Hence (A) is the correct answer.
answered Apr 10, 2014 by sreemathi.v
 

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