Complex Vector question (1 Viewer)

[cutemouse]

Hi, I've got a question. Could someone please help me?

Thanks =D

In the Argand diagram the points A, B, C and D represent the complex numbers α, β, γ and δ respectively.

(i) Describe the point which represents (1/2)(α+γ)

(ii) Deduce that if α+γ=B+δ then ABCD is a parrallelogram.

 

[shaon0]

Hi, I've got a question. Could someone please help me?

Thanks =D

In the Argand diagram the points A, B, C and D represent the complex numbers α, β, γ and δ respectively.

(i) Describe the point which represents (1/2)(α+γ)

(ii) Deduce that if α+γ=B+δ then ABCD is a parrallelogram.

i) (1/2)(a+c) is the midpoint of one of the diagonals.

ii) a+c=b+d
Thus, diagonals are equal and (a-b)=(c-d) (Thus, opposite sides are parallel to one another)
Thus, ABCD is a, parallelogram.

Also, (1/2)(a+c) maybe the pt of intersection of the diagonals but i cbf proving or disproving it right now.