Question

For complex numbers`z_1=x_1+iy_1" and " z_2=x_2+iy_2` we write `z_1 cap z_2` if `x_1 le X_2 and y_1 le y_2` Then for all compelx nubers z with `1 cap z` we have `(1-z)/(1+z) cap 0 `

Answer 1

Correct Answer - True
Let z=x iy `rArr 1 cap z "gives" 1 cap x+ iy `
or ` le x and o le y`
Given `(1-z)/(1+z) cap 0 rArr (1-x-iy)/(1+x+iy) cap 0 rArr ((1-x- iy)(1+x-iy))/((1+x+iy)(1+x-iy))cap0+0i`
`rArr (1-x^2-y^2)/((1+x)^2+y^2)-(2iy)/((1+y^2)+y^2)cap0 +0i`
`rArr x^2+y^2 ge 1`
and `-2y le0`
or `x^2+y^2 ge 1 and y ge 0 ` which is true by Eq.(i)