<prompt> Katika ndege changamano, z, z2, z3 huunda, kwa mpangilio fulani, wima tatu za mraba usioharibika. Ingiza maeneo yote yanayowezekana ya mraba, yakitenganishwa na koma.  <response>: Kwanza, zingatia hali ambapo z ni kati ya z2 na z3. Mchoro unaweza kuonekana kama ifuatavyo:asyukubwa wa kitengo sentimita 0.4;jozi z, zsquare, zcube, w;z 0,0;zsquare 5,-2;zcube 2,5;w zsquare zcube - z;choraz--zsquare,Arrow8;choraz--zcube,Arrow8;chorarightanglemarkzcube,z,zsquare,20;kuchorazcube--w--zsquare,dashed;leboz2 - z, z zsquare2, S;leboz3 - z, z zcube2, NW;nukta z, z, SW;nuktaz2, zsquare, SE;nuktaz3, zcube, NW;nukta w;asyMishale katika mchoro inalingana na nambari changamano z3 - z na z2 - z, ambazo ziko katika pembe ya 90circ kwa kila moja. Kwa hivyo, tunaweza kupata nambari moja changamano kwa kuzidisha nyingine kwa i. Hapa, z3 - z i z2 - z.Mchoro mwingine unaowezekana ni kama ifuatavyo:asyukubwa wa kitengo sentimita 0.4;jozi z, zsquare, zcube, w;z 0,0;zsquare 2,5;zcube 5,-2;w zsquare zcube - z;choraz--zsquare,Arrow8;choraz--zcube,Arrow8;chorarightanglemarkzcube,z,zsquare,20;kuchorazcube--w--zsquare,dashed;leboz2 - z, z zsquare2, NW;leboz3 - z, z zcube2, S;nukta z, z, SW;nuktaz2, zsquare, NW;nuktaz3, zcube, SE;nukta w;asyHapa, z3 - z -iz2 - z. Kwa hivyo, tunaweza kuchanganya milinganyo yote miwili kamaz3 - z pm i z2 - z.Tunaweza kubainisha kamazz - 1z 1 pm izz - 1.Kwa kuwa mraba haujabadilika, z neq 0 na z neq 1. Kisha tunaweza kugawanya kwa usalama. pande zote mbili kwa zz - 1, kupataz 1 pm i.Kwa z -1 i, eneo la mraba niz2 - z2 z2 z - 12 -1 i2 -2 i2 10.Kwa z -1 - i, eneo la mraba niz2 - z2 z2 z - 12 -1 - i2 -2 - i2 10.Kesi nyingine ni pale z2 ni kati ya z na z3.asyukubwa wa kitengo sentimita 0.4;jozi z, zsquare, zcube, w;z 2,5;zsquare 0,0;zcube 5,-2;w z zcube - zsquare;chorazsquare--z,Arrow8;chorazsquare--zcube,Arrow8;chorarightanglemarkz,zsquare,zcube,20;kuchoraz--w--zcube,dashed;leboz - z2, z zsquare2, NW;leboz3 - z2, zsquare zcube2, SSW;nukta z, z, NW;nuktaz2, zsquare, SW;nuktaz3, zcube, SE;nukta w;asyHii inatupa equationz3 - z2 pm i z - z2.Tunaweza kuainisha kamaz2 z - 1 pm izz - 1.Kisha z pm i.Kwa z i, eneo la mraba niz2 - z2 z2 z - 12 i2 i - 12 2.Kwa z -i, eneo la mraba niz2 - z2 z2 z - 12 -i2 -i - 12 2.Kesi ya mwisho ni pale z3 ni kati ya z na z2.asyukubwa wa kitengo sentimita 0.4;jozi z, zsquare, zcube, w;z 2,5;zsquare 5,-2;zcube 0,0;w z zsquare - zcube;chorazcube--z,Arrow8;chorazcube--zsquare,Arrow8;choraalama ya kuliaz,zcube,zsquare,20;kuchoraz--w--zsquare,dashed;leboz - z3, z zcube2, NW;leboz2 - z3, zsquare zcube2, SSW;nukta z, z, NW;nuktaz2, zsquare, SE;nuktaz3, zcube, SW;nukta w;asyHii inatupa equationz3 - z2 pm iz3 - z.Tunaweza kuainisha kamaz2 z - 1 pm i zz - 1z 1.Kisha z pm iz 1. Solving z iz 1. , tunapata z frac-1 i2. Kisha eneo la mraba niz3 - z22 z4 z - 12 kushoto frac-1 i2 kulia4 kushoto frac-3 i2 kulia2 frac14 cdot frac52 frac58.Kutatua z -iz 1, tunapata z frac-1 - i2. Kisha eneo la mraba niz3 - z22 z4 z - 12 kushoto frac-1 - i2 kulia4 kushoto frac-3 - i2 kulia2 frac14 cdot frac52 frac58.Kwa hiyo, maeneo yanayowezekana ya mraba ni frac58, 2, 10. 