Question

已知平行四邊形中,三個頂點對應的復數分別是2+i,4+3i,3+5i,求第四個頂點對應的復數.

Answer 1

解:如圖3-2-1,設點Z₁,Z₂,Z₃分別對應復數2+i,4+3i,3+5i.?

        圖3-2-1

(1)若Z₁Z₃為對角線,則=,?

即z₄-z₁=z₃-z₂,∴z₄=z₃-z₂+z₁=(3+5i)-(4+5i)+(2+i)=1+3i.?

(2)若Z₁Z₂為對角線,則=,?

即z₄-z₁=z₂-z₃,∴z₄=z₂-z₃+z₁=(4+3i)-(3+5i)+(2+i)=3-i.?

(3)若Z₂Z₃為對角線,則=,即z₄-z₂=z₃-z₁,?

∴z₄=z₃-z₁+z₂=(3+5i)-(2+i)+(4+3i)=5+7i.

點評:本題中平行四邊形共三種情況,故第四點對應的復數應有三解,要防止發生以偏概全的錯誤.