The points $z_1,z_2,z_3$ and $z_4$ in the complex plane are the vertices of a parallelogram taken in order, if and only if
Step-by-Step Solution
Key Concept: A quadrilateral is a parallelogram iff its diagonals bisect each other. For vertices in order $z_1,z_2,z_3,z_4$, the diagonals connect $z_1\leftrightarrow z_3$ and $z_2\leftrightarrow z_4$.
**Step 1: Use the diagonal midpoint property**
$z_1,z_2,z_3,z_4$ form a parallelogram (in order) iff the midpoints of the two diagonals coincide: $\dfrac{z_1+z_3}{2}=\dfrac{z_2+z_4}{2}$.
**Step 2: Write the condition**
$z_1+z_3=z_2+z_4$.
Correct Answer: 2