Question

The points z1,z2,z3;z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if

Answer 1

Answer:

$z_{1} + z_{3} = z_{2} + z_{4}$

Step-by-step explanation:

SInce, the points z1,z2,z3;z4 in the complex plane are the vertices of a parallelogram, we want to show that midpoint of its diagonal coincides.

If they represent vertices of a parallelogram then

midpoint of diagonal coincides.

Then we need to compute diagonal vertices and divide by two, and the condition is that both of the midpoints of diagonal are equal, thus, we have:

$\frac{z_{1} + z_{3} }{2} = \frac{z_{2} + z_{4} }{2}$

⇔ $z_{1} + z_{3} = z_{2} + z_{4}$

Answer 2

Answer:

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