The points A,B  and C  represent the complex numbers z1,z2,(1−i)z1+iz2  (where i=−1 ) respectively on the complex plane. The triangle ABC  is:

Since A=z1,B≡z2,C≡(1−i)z1+iz2 ∴      AB=|z1−z2|,BC=|(1−i)z1+iz2−z2| =|1−i||z1−z2|=2|z1−z2| and        CA=|(1−i)z1+iz2−z1| =|i||−z1+z2|=|z1−z2| ∴          AB=CA , and (AB)2+(CA)2=(BC)2 .