Show that the points A = 1 + 2i, B = 4 + 6i and C = -3 + 5i are the corners of a right-angled…

Step 1. Side AB. $B - A = 3 + 4i$, so $AB = 5$.

Step 2. Side AC. $C - A = -4 + 3i$, so $AC = 5$.

Step 3. Side BC. $C - B = -7 - i$, so $BC = \sqrt{49 + 1} = \sqrt{50} \approx 7.071$.

Step 4. Pythagoras. $AB^2 + AC^2 = 25 + 25 = 50 = BC^2$, so the angle at $A$ is a right angle.