If a ,b,c, and u,v,w are complex numbers repersenting the vertices of two triangle such that they are similar, then prove that `(a-c)/(a-b) =(u-w)/(u-v)`

Explanation

In the figure triangle ABC and PQR are similar.

`therefore (AC)/(PR) = (AB)/(PQ)`
`rArr (AC)/(AB) = (PR)/(PQ) `
`rArr |(a-c)/(a-b)| =|(u-w)/(u-v)| " "....(1)`
Also, `angle BAC = angleQPR`
` rArr arg((a-c)/(a-b)) = arg((u-w)/(u-v)) " ".....(2)`
Form (1) and (2), we get
`(a-c)/(a-b) = (u-w)/(u-v)`