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.

问题描述:

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.

∵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...