" 11."(cos theta+i sin theta)^(n)=cos n theta i+sin n theta

Prove,by induction,that (cos theta+i sin theta)^(n)=cos n theta+i sin n theta for all positive as well as negative integral values of

Prove that ((1+cos theta+i sin theta)/(1+cos theta-i sin theta))^(n)=cos n theta+i sin n theta

Using De Moivre 's theorem prove that : ((1+cos theta +i sin theta)/(1+cos theta - i sin theta))^n= cos n theta + i sin n theta , where i = sqrt(-1)

Prove the following by the method of induction for all n in N : (cos theta + i sin theta)^n = cos n theta + i sinntheta , where i = sqrt -1.

cos m theta-sin n theta=0

If (cos theta + i sin theta)(cos 2 theta +i sin 2 theta ) …(cos n theta + i sin n theta)=1 then the value of theta is (m are integers)-

The number of values of theta in (0, pi] , such that (cos theta + i sin theta) (cos 3 theta + i sin 3 theta) (cos 5 theta + i sin 5 theta) (cos 7 theta + i sin 7 theta) (cos 9 theta + i sin 9 theta) = -1 is

The value of (1+cos theta+i sin theta)^(n)+(1+cos theta-i sin theta)^n=