已知x，y∈R，且复数z1=x+y-30-xyi和复数z2=-|x+yi|+60i是共轭复数，设复数z1，z2在复平面内对应的点分别为A，B，又O为坐标原点，求△OAB的面积．

Question

已知x，y∈R，且复数z₁=x+y-30-xyi和复数z₂=-|x+yi|+60i是共轭复数，设复数z₁，z₂在复平面内对应的点分别为A，B，又O为坐标原点，求△OAB的面积．

Answer 1

∵复数z1=x+y-30-xyi和复数z2=-|x+yi|+60i是共轭复数，∴x+y-30=-|x+yi|，-xy=-60，即x+y-30=-x2+y2，xy=60．解得x=12、y=5，或 x=5，y=12．故复数z1 =-13-60i，复数z2=-13+60i．又复数z1，z2在复平面内对应的...