Learn Croatian: Imamo lošeg direktora.

The verb imamo (we have) requires its object to be in the accusative case. Because direktor is a living masculine noun, it takes the animate ending -a to become direktora. The adjective modifying it must match this animate form, so loš also changes.

Why does loš become lošeg instead of lošog?

For animate masculine nouns, adjectives usually add -og in the accusative case. However, if the adjective's base ends in a soft sound like š, č, ć, ž, or j, the ending changes from -og to -eg. Since loš ends in š, it becomes lošeg.

Where is the word for 'we' in this sentence?

In Croatian, you usually drop subject pronouns like mi (we) because the verb itself tells you who is doing the action. The -mo ending on imamo already means we have.

What are the base dictionary forms of these words?