15.设 $z_{1}, z_{2} \in \mathbf{C}$,则"$z_{1}, z_{2}$ 均为实数"是"$z_{1}-z_{2}$ 是实数"的.
参考答案A
2015_上海卷 (2015·文)
15.设 $z_{1}, z_{2} \in \mathbf{C}$,则"$z_{1}, z_{2}$ 均为实数"是"$z_{1}-z_{2}$ 是实数"的.
【答案】A
【解析】设 $z_{1}=a_{1}+b_{1} i\left(a_{1}, b_{1} \in \mathbf{R}\right), z_{2}=a_{2}+b_{2} i\left(a_{2}, b_{2} \in \mathbf{R}\right)$,若 $z_{1}, z_{2}$ 均为实数,则 $b_{1}=b_{2}=0$,所以 $z_{1}-z_{2}=a_{1}-a_{2}+\left(b_{1}-b_{2}\right) i=a_{1}-a_{2}$ 是实数;若 $z_{1}-z_{2}=a_{1}-a_{2}+\left(b_{1}-b_{2}\right) i$ 是实数,则 $b_{1}=b_{2}$,
所以"$z_{1}$、 $z_{2}$ 均为实数"是"$z_{1}-z_{2}$ 是实数"的充分非必要条件,选 A.
【考点定位】复数的概念,充分条件、必要条件的判定.