Geometrical applications for complex numbers (1 Viewer)

[Joshmosh2]

If the points A,B,C,D represent the complex numbers α,β,γ,δ respectively and

(a) α+γ=β+δ , show that the points are vertices of a parallelogram

 

[FrankXie]

If the points A,B,C,D represent the complex numbers α,β,γ,δ respectively and

(a) α+γ=β+δ , show that the points are vertices of a parallelogram

There are usually two different ways to solve this type of question.



the LHS represents the midpont of AC, while the RHS represents the midpont of BD. This equation means AC and BD bisect each other, hence ABCD is a parallelogram.



the LHS represents the vector AB while the RHS represents the vector DC. This equation means the vectors have same magnitude and direction. Therefore AB is parallel to DC and equal to DC in length. So ABCD is a parallelogram.