Question

If the complex numbers \( z_1, z_2 \) and \( z_3 \) denote the vertices of an isosceles triangle, right angled at \( z_1 \), then \( (z_1 - z_2)^2 + (z_1 - z_3)^2 \) is equal to:

• A. \( 0 \)
• B. \( (z_2 + z_3)^2 \)
• C. \( 2 \)
• D. \( 3 \)
• E. \( (z_2 - z_3)^2 \)

Hint:

For any right-angled triangle at $z_1$, the ratio of $(z_3-z_1)/(z_2-z_1)$ is purely imaginary ($ki$). If it's isosceles, $k = \pm 1$.

Answer 1

The Correct Option is A