Question

1p 3. Fie z = 5-i 3+ 2i Aflati Re(z) si z (modulul lui z)​

Answer 1

z = (5-i) / (3+2i) amplificat cu 3-2i

= (5-i)(3-2i) / (3+2i)(3-2i) = (15-10i-3i+2i²) / (9+4) = (15-13i-2) / 13 = (13-13i) / 13 = 13(1-i) / 13 = 1-i

Re(z) = 1

|z| = V(1² + (-1)²) = V(1+1) = V2

|z| = V2