Let $z_1$ be a purely imaginary complex number and $z_2$ be any complex number such that $|z_1 + z_2| = |z_1 - z_2|$. Find the circumcentre of the triangle with vertices $0, z_1, z_2$.
(A) $z_1/2$ (B) $z_2/2$ (C) $(z_1 + z_2)/2$ (D) $(z_1 - z_2)/2$
(C) The circumcentre is $(z_1 + z_2)/2$.
Let $z_1$ be a purely imaginary complex number and $z_2$ be any complex number such that $|z_1 + z_2| = |z_1 - z_2|$. Find the circumcentre of the triangle with vertices $0, z_1, z_2$.

(A) $z_1/2$ \quad (B) $z_2/2$ \quad (C) $(z_1 + z_2)/2$ \quad (D) $(z_1 - z_2)/2$