Question

Determinati z=x+iy, daca 2z=|z|+2i

Answer 1

$2(x+iy)= \sqrt{x^2+y^2} +2i \\ 2x= \sqrt{x^2+y^2} \\ 2y=2 \\ y=1 ;si:4 x^{2} = x^{2} +1 \\ y=1;si:3 x^{2} =1 \\ y=1;si:x= \frac{1}{ \sqrt{3} } \\ sau \\ y=1;si:x=- \frac{1}{ \sqrt{3} } \\ z= \frac{1}{ \sqrt{3} } +i;sau:z=- \frac{1}{ \sqrt{3} }+i$