Question

va rog mult.. a) si d) sau macar unul...

Answer 1

a.  | z-1 |=| z-1-i| <=> z-1=-z+1+i <=> z-(-z)-1-1-i=0 <=> 2z-2-i=0 <=> 2z-2=i <=> 2·(z-1)=i <=> 2·(a+bi-1)=i => a=4 si b=3 => |z|=√ a² +b² =5 => |z|=5 ;

d.  | z-1+i |=2 <=> -2 <= z-1+i <= 2 <=> -1 <= z+i <= 3 <=> -1 <= a+bi+i <=3 <=> -1 <= a+i·(b+1) <=3 => a=12 si b=5 => |z|=√ a² +b² =13 => |z|=13 .