# Thread: More Complex Analysis help.

1. ## More Complex Analysis help.

Prove that if K in the complex plane is compact and f(z) and g(z) are uniformly continuous functions on K, then f(z)g(z) is uniformly continuous on K.

2. Originally Posted by grad444
Prove that if K in the complex plane is compact and f(z) and g(z) are uniformly continuous functions on K, then f(z)g(z) is uniformly continuous on K.
Since f amd g are continous on K so is f*g.
But since f*g is continous on a compact set it is automatically uniformly continous.