Given triangle ABC, D is the foot of the perpendicular from A to BC. Find the coordinates of D as a complex coordinate.
Given
(I need this to solve a bigger problem.)
Remember you can think of complex numbers are vectors too. What we shall do is project the line segment onto . In vector terms we shall find the projection of onto .
Remember and the dot product for complex numbers is .
Therefore, the projection is,
This simplifies to, (which is of course a real number).
Therefore, is the projected vector.
Therefore, .