  In the paper the complex geodesics of a convex domain in $\mathbb C^n$ are
studied. One of the main results of the paper provides certain necessary
condition for a holomorphic map to be a complex geodesic for a convex domain in
$\mathbb C^n$. The established condition is of geometric nature and it allows
to find a formula for every complex geodesic. The $\mathbb C$-convexity of
semitube domains is also discussed.
