Question

已知复数Z.=3+2i 复数z满足Z.*z=3z+Z.则复数z等于?

Answer 1

设z=a+bi

则(3+2i)(a+bi)=3(a+bi)+3+2i

即(3a-2b)+(2a+3b)i=(3a+3)+(3b+2)i

所以3a-2b=3a+3,2a+3b=3b+2

故a=1,b=-3/2

所以z=1-3i/2