<prompt> Mizizi minne changamano ya2z4 8iz3 -9 9iz2 -18 - 2iz 3 - 12i 0, inapopangwa katika ndege changamano, tengeneza rhombus. Pata eneo la rhombus.  <response>: Acha a, b, c, d iwe mizizi ya quartic. Acha A iwe sehemu inayolingana na nambari changamano a, n.k.Acha O iwe kitovu cha rhombus. Kisha nambari changamano inayolingana na O ni wastani wa a, b, c, d. Kulingana na fomula za Vieta, a b c d -frac8i2 -4i, kwa hivyo wastani wao ni frac-4i4 -i. Kwa hivyo, O iko -i.asyukubwa wa kitengo 2 cm;jozi A, B, C, D, O;A -1.3362,0.8539;C 1.3362,-2.8539;D -0.5613,-1.4046;B 0.5613,-0.59544;O A C2;nukta A, A, NW;nuktaB, B, NE;nukta C, C, SE;nukta D, D, SW;nuktaO, O, S;kuchoraA--B--C--D--mzunguko;kuchoraA--C;choraB--D;lebop, A O2, SW, nyekundu;leboq, B O2, SE, nyekundu;asyHebu p OA na q OB. Kisha tunataka kukokotoa eneo la rhombus, ambalo ni 4 cdot frac12 pq 2pq.Tunaona kwamba p a i c i na q b i d i.Kwa kuwa a, b, c, d ndio mizizi ya quartic katika tatizo, tunaweza kuandika2z4 8iz3 -9 9iz2 -18 - 2iz 3 - 12i 2z - az - bz - c z - d.Kuweka z -i, tunapata4 - 3i 2-i - a-i - b-i - c-i - d.Tukichukua thamani kamili ya pande zote mbili, tunapata5 2 a ib ic id i 2p2 q2.Kisha 4p2 q2 10, hivyo 2pq sqrt10. 