Let $P(e^{i\theta_1})$, $Q(e^{i\theta_2})$ and $R(e^{i\theta_3})$ be the vertices of a triangle PQR in the Argand Plane. The orthocenter of the triangle PQR is

$P,Q,R$ lie on the unit circle and hence origin is the circumcenter, The centroid is easily found as $\dfrac{(p+q+r)}{3}$,Using euler line theorem that centroid divides the line joining the orthocenter and circumcenter in the ratio of $2:1$

Let orthocenter be $x,y$

$Using \quad section \quad formula;$

$Re(\dfrac{(p+q+r)}{3})=\dfrac{(1.x+2.0)}{3}$

$Im(\dfrac{(p+q+r)}{3})=\dfrac{(1.y+2.0)}{3}$

we get orthocenter as

$p+q+r\rightarrow$ $e^{\theta_1}+$$e^{\theta_2}+$$e^{\theta_3}$