Question

已知復(fù)平面內(nèi)平行四邊形ABCD,點(diǎn)A 對應(yīng)的復(fù)數(shù)為向量對應(yīng)的復(fù)數(shù)為向量對應(yīng)的復(fù)數(shù)為
(1)求點(diǎn)C,D對應(yīng)的復(fù)數(shù);
(2)求平行四邊形ABCD的面積.

Answer 1

（1）點(diǎn)C對應(yīng)的復(fù)數(shù)為(2+i)+(2-3i)="4-2i," D對應(yīng)的復(fù)數(shù)為5.
（2）平行四邊形ABCD的面積是

(1)因?yàn)橄蛄?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135657806246.gif" style="vertical-align:middle;" />對應(yīng)的復(fù)數(shù)為1+2i,向量對應(yīng)的復(fù)數(shù)為3-i,所以向量對應(yīng)的復(fù)數(shù)為(3-)-(1+2)=2-3,又=+,所以點(diǎn)C對應(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對應(yīng)的復(fù)數(shù)為5.
(2) 因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823135658118255.gif" style="vertical-align:middle;" />=所以  所以S=.所以平行四邊形ABCD的面積是7.