Question

The points $z_1=3+\sqrt{3}i\text{and}{z}_2=2\sqrt{3}+6i$ are given on a complex plane. The complex number lying on the bisector of the angle formed by the vector $z_1$ and $z_2$ is

• A. $z=\frac{(3+2\sqrt{3})}{2}+\frac{\sqrt{3}+2}{2}i$
• B. $z=5+5i$
• C. $z=\frac{(3+2\sqrt{3})}{2}-\frac{\sqrt{3}+2}{2}i$
• D. $z=(3+3\sqrt{3})+2i$

Answer 1

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

Note that $z_1=3+\sqrt{3}i$ lies on the line $y=\left(1/\sqrt{3}\right)x\text{and}{z}_2=2\sqrt{3}+6i$ lies on the line $y=\sqrt{3}x$


Now from diagram, Equation of angular bisectors will be $y=\pm x$
Hence from the given options ,$z=5+5i$ will only lie on the bisector of $z_1$ and $z_2$, i.e., $y=x$.