Prove, by induction, that `(cos theta + isintheta)^n = cos n theta + isin ntheta` for all positive as well as negative integral values of

If (1 + cos theta + isin theta) (1 + cos 2 theta + isin 2theta) = x + iy then y =

(cos3theta+isin3theta)^5/(costheta+isintheta)^6

Prove that (frac(1+costheta+isintheta)(1+costheta-isintheta))^n=cos ntheta+isin ntheta .

Solve the following:Show that (costheta+isintheta)^3=cos3theta+isin3theta

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

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

If (1+costheta+isintheta)(1+cos2theta+isin2theta)=x+iy then y =

cos theta + cos 2 theta + cos 3 theta + …. + cos { (n-1) theta}+ cos n theta=

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

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.