Question

已知復(fù)平面內(nèi)平行四邊形ABCD,點(diǎn)A 對(duì)應(yīng)的復(fù)數(shù)為向量對(duì)應(yīng)的復(fù)數(shù)為向量對(duì)應(yīng)的復(fù)數(shù)為

(1)求點(diǎn)C,D對(duì)應(yīng)的復(fù)數(shù);

(2)求平行四邊形ABCD的面積.

Answer 1

（1）點(diǎn)C對(duì)應(yīng)的復(fù)數(shù)為(2+i)+(2-3i)=4-2i, D對(duì)應(yīng)的復(fù)數(shù)為5.

（2）平行四邊形ABCD的面積是

解析:

(1)因?yàn)橄蛄?img width=25 height=23 src="http://thumb.1010pic.com/pic1/1899/sx/12/290012.gif" >對(duì)應(yīng)的復(fù)數(shù)為1+2i,向量對(duì)應(yīng)的復(fù)數(shù)為3-i,所以向量對(duì)應(yīng)的復(fù)數(shù)為(3-)-(1+2)=2-3,又=+,所以點(diǎn)C對(duì)應(yīng)的復(fù)數(shù)為(2+i)+(2-3i)=4-2i,又=+=(1+2i)+(3-i)=4+i,=-=2+i-(1+2i)=1-i,所以=+=1-i+(4+i)=5,所以D對(duì)應(yīng)的復(fù)數(shù)為5.

(2) 因?yàn)?img width=31 height=23 src="http://thumb.1010pic.com/pic1/1899/sx/30/290030.gif" >=所以  所以S=.所以平行四邊形ABCD的面積是7.