Hello, stud_02!

How about a geometric proof?

and are complex numbers in argand diagram and is the origin.

Show and are perpendicular if: .Code:Q * - - - - - - - - - - - * R / * * / / * * / / * * / Z2 / * / / * * / / * * / / * * / O * - - - - - - - - - - - * P Z1

Then: .

Hence .

If , then: .

. . And we have a parallelogram with equal diagonals.

A parallelogram with equal diagonals is a.rectangle

. . Therefore: .