Question

If z₁ = 2 – i,  z₂ = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`

Answer 1

`z_1  = 2  - i,  z_2  = 1  +  i`

∴ `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|  = |((2-i)+(1 + i)+1)/((2-i) - (1 + i) + 1)|`

= `|4/(2-2i)|  =  |4/(2(1 - i))|`

= `|2/(1 - i) xx (1 + i)/(1 + i)|  =  |(2(1 + i))/(1^2 - i^2)|`

= `|(2(1 + i))/(1 + 1)|`      [i²  = - 1]

= `|(2(1 +i))/2|`

= `1 + i = sqrt(1^2  + 1^2)  = sqrt2`

The value of this type is `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)| "is" sqrt2`