Please answer this question in detail formate.

Thankyou.

basically what we wanna prove is (z1 – z2)/(z3 – z2)= 2(z3 – z1)/(z2 – z1)

now, modulus of both sides is same, and is equal to root 2. this is because of the properties of a isosceles triangle and pythagoras theorem.

now, as regards the argument, we make use of rotation theorem in complex plane. we see that argument if LHS is – 45 degree. similarly argument of (z3 – z1)/(z2 – z1) is – 45 degree. but that implies that argument of 2(z3 – z1)/(z2 – z1) is – 45 degree as well. since the modulus as well as the argument of the sides match we conclude that both sides are equal to each other. QED