Find the value of (1 + i)4 (1 + 1/i)4
(1+i)4 = [(1+i)2]2
= [ 1 + i2 + 2i ]2
Here i2= -1
= (1 - 1 + 2i)2 = 4i2 = -4
.
And,
(1 + 1/i)4 = [ (1 + 1/i)2 ]2
= [ 1 + (1/i)2 + 2(1/i) ]2
= [ 1 + (1/-1) + (2/i) ]2
= [ 1 - 1 + (2/i) ]2
= (2/i)2 = 4/i2 = 4/-1 = -4
.
Therefore replacing the values in the question:-
(1+i)4 (1 + 1/i)4 = (-4) * (-4) = 16
.
Hence answer is 16