Question

how does Fundamental duties complement fundamental rights

Answer 1

Fundamental right of peaceful living condition is solely dependent upon mutual survival.  while Fundamental duties were just the unwritten agreement.
for example
Just imagine if one keep triggering venom from his mouth until when you keep continue living with him peacefully? It is right of mine to open up this thing. and to control my tongue for living peacefully is the fundamental duty 

Answer 2

Answer:

Fundamental Duties complement Fundamental Rights

Our rights are rules of interaction among people. They place constraints and obligations upon the actions of the state and individuals or groups. Rights are defined as claims of an individual that are essential for the development of his or her own self and that are recognized by society or State. These are legal, social, or ethical principles of freedom or entitlement and are the fundamental normative rules about what is allowed to people or owed to people, according to some legal system, social convention, or ethical theory. Rights are considered fundamental to civilization, being regarded as established pillars of society and culture. But the rights have real meaning only if individuals perform duties. A duty is something that someone is expected or required to do. Life can be balanced if rights and duties go hand in hand and become complementary to each other. Rights are what we want others to do for us whereas the duties are those acts which we should perform for others. Thus, a right comes with an obligation to show respect for the rights of others. The obligations that accompany rights are in the form of duties. If we have the right to enjoy public facilities like transport or health services, it becomes our duty to allow others to avail the same. If we have the right to freedom, it becomes our duty not to misuse this and harm others. Hence the Fundamental Rights and Fundamental Duties enshrined in the Constitution are equally important and they complement each other.