In the 1800s, what new technology helped imperial nations communicate quickly with their colonies in other parts of the world?

Telegraph

Explanation:

Prior to the creation of Telegraph, the only method that people in the colonies could use to communicate was letters. But it took a really long time for a person to reach another person who live in another country with letters. Not only that, the contain of a letter could easily fabricated by a third party. This created a lot of problems for the users/

Telegraph was commonly used since 1840. It's regarded as the fastest method to send a message before the telephone was invented. It's designed to send a set of codes of electric current through dedicated wires and the received could decipher those codes into a full message.

rosevelt. 1973. "slaves everywhere"