Luke 3:8 states prove by the way you live that you have repented of your sins and turned to God.
Our lives here on earth will never be perfectly lives, as we are sinful by nature. However, when we become Christians and repent of our sins, our life should show that to others. As we turn to God, those sins of habitual nature should lessen and cease. People should be able to look at our lives before and after Christ and see a difference.
Yes, we are forgiven, but our life should demonstrate change and growth. Our live should have fruit that shows we are Christ's chosen. If it does not, we will eventually be shopped down and cast into the fire (Luke 3:9).