z=(2cosx+2)+(2sinx+√5)i

z- 1 =(2 cosx+ 1)+(2 sinx+√5)I

z+ 1 =(2 cosx+3)+(2 sinx+√5)I

|z- 1|^2+|z+ 1|^2

=(2cosx+ 1)^2+(2cosx+3)^2+2(2sinx+√5)^2

= 16cosx+8√5sinx+28

& lt=24+28=52

| z- 1 | 2 +| z+ 1 | 2 The maximum value is 52.