复数Z=x+yi(x,y属于R),满足x/1-i+y/1-2i=5/1-3i,求Z^2-2乘以Z的共轭复数的值

Question

复数Z=x+yi(x,y属于R),满足x/1-i + y/1-2i = 5/1-3i ,求Z^2 - 2乘以Z的共轭复数的值

Answer 1

x/1-i=x(1+i)/2
y/1-2i =y(1+2i)/5
5/1-3i =5(1+3i)/10
x/1-i + y/1-2i =(5x+5xi+2y+4yi)/10=5(1+3i)/10
5x+2y=5
5x+4y=15 y=5 x=-1
z=-1+5i
Z的共轭=-1-5i
Z^2 - 2乘以Z=-24-10i+2+10i=-22