If end points of diagonal AC of a square ABCD are A(z) and C(w) on a argand plane , then what is the incentre of triangle ABC .
My try
let A be on y axis , C be on x axis and B is origin .
Let $A=ia$ then $w=a$
and argument of incentre would be $\pi /4$
but now how to proceed .
Answer is given as $\frac {z+w}{2}+i\frac{z-w}{2}(\sqrt 2 -1)$
HINT: So far, so good.
You may find the center$(O_x,O_y)$ by using: $$O_x=\frac{aA_x+bB_x+cC_x}{a+b+c}$$ $$O_y=\frac{aA_y+bB_y+cC_y}{a+b+c}$$
You already have Coodinates of A,B and C. You know the length of a,b,c.
Although. My answer doesn't seem to provide you in terms of $w,z$ immediately. You have to convert it.
Suggestions are welcomes in improvement.