Complex Analysis: Theory and Applications · Problem 1.2.6

Complex Numbers — Howell & Matthews

Mathematics — Complex Analysis · real-imaginary-parts-properties

Problem

Let z1=(x1,y1)z_1 = (x_1, y_1) and z2=(x2,y2)z_2 = (x_2, y_2) be arbitrary complex numbers. Prove or disprove the following. (a) Re(z1+z2)=Re(z1)+Re(z2)\text{Re}(z_1 + z_2) = \text{Re}(z_1) + \text{Re}(z_2). (b) Re(z1z2)=Re(z1)Re(z2)\text{Re}(z_1 z_2) = \text{Re}(z_1)\text{Re}(z_2). (c) Im(z1+z2)=Im(z1)+Im(z2)\text{Im}(z_1 + z_2) = \text{Im}(z_1) + \text{Im}(z_2). (d) Im(z1z2)=Im(z1)Im(z2)\text{Im}(z_1 z_2) = \text{Im}(z_1)\text{Im}(z_2).

Related theory

Browse the problem library