is it true that if g(z) and h(z) are continuous functions on C and

lim z->infinity of g(z)= infinity

lim z->infitity of h(z) = infinity

is it always true that lim z->infinity (g(z)+h(z)) = infinity?

I dont think this is true. but im having difficulties coming up with counterexample. so starting to think its possibily true??