已知复数Z满足:|Z|=1+3i-Z,求[(1+i)^2(3+4i)^2]/2Z
问题描述:
已知复数Z满足:|Z|=1+3i-Z,求[(1+i)^2(3+4i)^2]/2Z
答
|Z|=1+3i-Z设z=x+yi|z|=√(x^2+y^2)|Z|=1+3i-Z,√(x^2+y^2)=(1-x)+(3-y)i∴√(x^2+y^2)=1-x,且3-y=0∴y=3√(x^2+9)=1-x x^2+9=(1-x)^29=1-2x,x=-4,符合题意∴z=-4+3i∴[(1+i)^2(3+4i)^2]/2Z=[2i(-7+24i)]/[2(-4+3i)]...