A living cell can be best studied by the means of

• Since we need to use staining to study the living cells and because there's always a possibility of incurring harm upon these cells we use the phase-contrast microscope. 
• There was no requirement of any staining on the living cells and can be visualised in its original state. 
• The constructive interference gives an image with high contrast and every minute detail can be observed. 
• This technique also helps us to observe the living cell in its natural state.

Hence, option C is the correct answer.