positive real number

Simplify the following:
(i + 1)^16

(1 + i)^16 = ((i + 1)^8)^2 = (((i + 1)^4)^2)^2 = ((((i + 1)^2)^2)^2)^2:
((((i + 1)^2)^2)^2)^2

(i + 1)^2 = 1 + i + i - 1 = 2 i:
(((2 i)^2)^2)^2

(2 i)^2 = -4:
((-4)^2)^2

(-4)^2 = 16:
16^2

 =256