1-cos theta+i sin theta

Express each one of the following in the standard form a+ib (1)/(1-cos theta+2i sin theta)

Express each one of the following in the standard form a+ib , 1/(1-cos theta+2i sin theta) .

Express (1)/(1-cos theta+2i sin theta) in the form of a+ib .

Express (1)/(1-cos theta+2i sin theta) in the form x+iy.

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

if alpha and beta the roots of z+ (1)/(z) =2 (cos theta + i sin theta ) where 0 lt theta lt pi and i =sqrt(-1) show that |alpha - i |= | beta -i|

((cos theta + i sin theta) / (sin theta + i cos theta)) ^ (4) = cos8 theta + i sin8 theta