Olympiad Number Theory · Superchallenge problem

Points $a, b, c$ lie on the unit circle in the complex plane with $a = 1$, $b = i$, $c = -\dfrac{3}{5} - \dfrac{4}{5}i$. The orthocenter of triangle $abc$ is $h = a + b + c$. Compute $|h|^2$. Express your answer as a common fraction.