The point `z_1=3+sqrt(3)i` and `z_2=2sqrt(3)+6i` are given on a complex plane. The complex number lying on the bisector of the angel formed by the vectors `z_1a n dz_2` is `z=((3+2sqrt(3)))/2+(sqrt(3)+2)/2i` `z=5+5i` `z=-1-i` none of these

Options

A. `z= ((3+2sqrt(3)))/(2) +(sqrt(3)+2)/(2)i`
B. `z=5+5i`
C. `z=- 1-i`
D. none of these

Answer

B

Explanation

Note that `z_(1) = 3 +sqrt(3i)` lies on the line `y = (1//sqrt(3))x` and
`z_(2) = 2sqrt(3) + 6i` lies on the lies on the line ` y = sqrt(3)x`.
Hence, `z = 5 + 5i` will not lie on the bisector of `z_(1)` and `z_(2)` i.e., y= x