Using the mathematical induction, show that for any natural number n, with the assumption `i^(2)=-1`,`(r(costheta+isintheta))^(n)=r^(n)(cosntheta+isinntheta)`

Answer

This implies, P(k+1) is true. The validity of P(k+1) followos from that of P(k) Therefore by the principle of mathematical induction , for any natural number n.
`(r(costheta+isintheta))^(n)=r^(n)(cosntheta+isinntheta)`