Question

于任意的两个复数对(a,b),(c,d),定义运算(a,b)*(c,d)=ad-bc

若（1，-1）*（z，zi）=1-i ，求复数z

Answer 1

设z=a+bi, 则zi=ai+bi�0�5=ai-b∴(1,-1)*(z,zi)=zi-(-z)=ai-b+a+bi=(a-b)+(a+b)i=1-i∴a-b=1, a+b=-1解得 a=0,b=-1∴z=a+bi=-i

Answer 2

zi+z=1-i z=(1-i)/(1+i)=(1-i)(1-i)/(1+i)(1-i)=-2i/2=-i