Question

The points $z_1=3+\sqrt{3}iand{z}_2=2\sqrt{3}+6i$ are given on a complex plane. The complex number laying on the bisector of the angle formed by the vectors $z_{1}and{z}_2$ is

• A. $z=\frac{(3+2\sqrt{3})}{2}+\frac{\sqrt{3}+2}{2}i$
• B. $z=5+5i$
• C. $z=-1-i$
• D. none

Answer 1

The correct option is B $z=5+5i$

$z_1=3+\sqrt{3}i$

$z_2=2\sqrt{3}+6i$

Consider, $z=z_1+z_2$

$=(3+\sqrt{3}i)+(2\sqrt{3}+6i)$

$=(3+2\sqrt{3})+i(\sqrt{3}+6)$

$=[3^2+{\left(2\sqrt{3}\right)}^2]+i[{\sqrt{3}}^2+6^2]$

$=\frac{15+15i}{3}$

$=5+5i$

Hence, the answer is $5+5i.$