The point ` z_(1),z_(2),z_(3),z_(4)` in the complex plane are the vertices of a parallogram taken in order, if and only if.
` (1) z _(1) +z_(4)=z_(2)+z_(3)` (2) ` z_(1)+z_(3) =z_(2) +z_(4)`
(3) ` z_(1)+z_(2) =z_(3)+z_(4)` (4) ` z_(1) + z_(3) ne z_(2) +z_(4)`

Answer

To determine the condition under which the points \( z_1, z_2, z_3, z_4 \) in the complex plane form the vertices of a parallelogram, we can use the property of midpoints of the diagonals of a parallelogram.

### Step-by-step Solution:

1. **Understanding the Midpoint Condition**:
In a parallelogram, the midpoints of the diagonals are equal. The diagonals in this case are formed by the points \( z_1, z_3 \) and \( z_2, z_4 \).

2. **Finding the Midpoints**:
- The midpoint of the diagonal connecting \( z_1 \) and \( z_3 \) is given by:
\[ \text{Midpoint of } z_1 \text{ and } z_3 = \frac{z_1 + z_3}{2} \]
- The midpoint of the diagonal connecting \( z_2 \) and \( z_4 \) is given by:
\[ \text{Midpoint of } z_2 \text{ and } z_4 = \frac{z_2 + z_4}{2} \]

3. **Setting the Midpoints Equal**:
Since the midpoints of the diagonals must be equal, we set the two expressions equal to each other:
\[ \frac{z_1 + z_3}{2} = \frac{z_2 + z_4}{2} \]

4. **Eliminating the Denominator**:
To eliminate the denominator, we can multiply both sides by 2:
\[ z_1 + z_3 = z_2 + z_4 \]

5. **Rearranging the Equation**:
Rearranging the equation gives us:
\[ z_1 + z_3 - z_2 - z_4 = 0 \]
This can be rewritten as:
\[ z_1 + z_3 = z_2 + z_4 \]

6. **Identifying the Correct Option**:
From the options provided in the question, we can see that option (2) states:
\[ z_1 + z_3 = z_2 + z_4 \]
Therefore, this is the correct condition for the points \( z_1, z_2, z_3, z_4 \) to be the vertices of a parallelogram.

### Conclusion:
The correct answer is option (2): \( z_1 + z_3 = z_2 + z_4 \).