在平行四邊形ABCD中,點(diǎn)A,B,C分別對(duì)應(yīng)的復(fù)數(shù)為2+i,4+3i,3+5i,則點(diǎn)D對(duì)應(yīng)的復(fù)數(shù)為_(kāi)_____.
設(shè)點(diǎn)D對(duì)應(yīng)的復(fù)數(shù)為x+yi,x、y∈R,由題意可得
對(duì)應(yīng)的復(fù)數(shù)等于
對(duì)應(yīng)的復(fù)數(shù).
對(duì)應(yīng)的復(fù)數(shù)為(4+3i)-(2+i)=2+2i,
對(duì)應(yīng)的復(fù)數(shù)為 (3+5i)-(x+yi)=3-x+(5-y)i,
故有 2+2i=3-x+(5-y)i,解得 x=1,y=3,故點(diǎn)D對(duì)應(yīng)的復(fù)數(shù)為1+3i,
故答案為 1+3i.