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For any two complex numbers Z1 and Z2, which of the following results is true?
1. |Z1 - Z2| < |Z1| - |Z2|
2. |Z1 - Z2| < ||Z1| - |Z2||
3. |Z1 + Z2| < ||Z1| - |Z2||
4. |Z1 + Z2|2 + |Z1 - Z2|2 = 2(|Z1|2 + |Z2|2)

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Best answer
Correct Answer - Option 4 : |Z1 + Z2|2 + |Z1 - Z2|2 = 2(|Z1|2 + |Z2|2)

Explanation:

We know that:

|Z1 + Z2|2  = |Z1|2 + |Z2|2  + Re (Z1Z2) ....(i)

|Z1 - Z2|2  = |Z1|2 + |Z2|2  - Re (Z1Z2) ....(ii)

By adding equation (i) and equation (ii)

|Z1 + Z2|2 + |Z1 - Z2|2  =  |Z1|+ |Z2|2 + Re (Z1Z2) + |Z1|2 + |Z2|2  - Re (Z1Z2)

|Z1 + Z2|2 + |Z1 - Z2|2  = |Z1|2 + |Z2|2  + |Z1|2 + |Z2|2

|Z1 + Z2|2 + |Z1 - Z2|2  = 2(|Z1|2 + |Z2|2)

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