i will let theta equal x to make it simply for me
z = cosx + isinx,
z + 1 = cosx + 1 + isinx, to eliminate the 1 use cosx = 2cos^2(x/2) - 1 and also sub sinx = 2sin(x/2)cos(x/2)
z + 1 = 2cos^2(x/2) - 1 + 1 + 2isin(x/2)cos(x/2) ...now we can factor cos(x/2) out and the first part is done
z...