When theta=0, you have q = cos(0) + sin(0)*(ai+bj+ck) = 1 + 0 = 1 That means applying the "rotation" to the vector gives v' = q * v * q^-1 = 1 * v * 1^-1

When theta=0, you have q = cos(0) + sin(0)*(ai+bj+ck) = 1 + 0 = 1 That means applying the "rotation" to the vector gives v' = q * v * q^-1 = 1 * v * 1^-1 = v So the output ("rotated") vector is the same as the input, as you would expect for a rotation by 0.