Bună! ⭐
_________
[tex]z=a+bi[/tex]
_________
[tex](1-i)z=1+i <=>[/tex]
[tex]<=> (1-i)(a+bi)=1+i <=>[/tex]
[tex]<=> a+bi-ai-bi^{2} =1+i <=>[/tex]
[tex]<=> a+bi-ai+b=1+i <=>[/tex]
[tex]<=> a+b+i (b-a)=1+i =>[/tex]
[tex]=> a+b=1[/tex] [tex]si[/tex] [tex]b-a=1[/tex]
[tex]\left \{ {{a+b=1} \atop {-a+b=1}} \right.[/tex]
[tex]====(+)[/tex]
[tex]/ 2b=2 / :2=> b=1[/tex]
[tex]a+b=1 <=> a+1=1 / -1 => a=0[/tex]
__________
[tex]z=i[/tex]
