However, if the complaint is serious, then dealing with it rapidly is more important than getting it in writing.
No tribunal judge will give you extra credit for waiting for a complaint in writing if the person making the complaint is in distress.
Also, not all complaints have to come from the employee. Often employees are fearful of making formal complaints due to fear of the repercussions.
You have a duty of care to the employee to investigate the complaint regardless of how the information has come to you.