question_answer

Which of the following are correct for any two complex numbers \[{{z}_{1}}\] and \[{{z}_{2}}\] [Roorkee 1998]

A) \[|{{z}_{1}}{{z}_{2}}|\,=\,|{{z}_{1}}||{{z}_{2}}|\]

B)   \[arg\,\,({{z}_{1}}{{z}_{2}})=(arg\,{{z}_{1}})(arg\,{{z}_{2}})\]

C) \[|{{z}_{1}}+{{z}_{2}}|\,=\,|{{z}_{1}}|+|{{z}_{2}}|\]

D) \[|{{z}_{1}}-{{z}_{2}}|\,\ge \,|{{z}_{1}}|-|{{z}_{2}}|\]