question_answer

If\[{{z}_{1}}\]and\[{{z}_{2}}\]are any two complex numbers, then which one of the following is true?

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

B)                         \[|{{z}_{1}}-{{z}_{2}}|=|{{z}_{1}}|-|{{z}_{2}}|\]

C)                         \[|{{z}_{1}}-{{z}_{2}}|\le |{{z}_{1}}|+|{{z}_{2}}|\]

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

E)                         \[\left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|\ne \left| \frac{{{z}_{1}}}{{{z}_{2}}} \right|,\]where\[{{z}_{2}}\ne 0\]