Correct Answer - Option 3 : 32
CONCEPT:
Let x and y be any two real numbers, then any number of the form x + iy is called a complex number, where i = √-1 or i2 = -1
CALCULATION:
Here, we have to evaluate the expression: (1 + i)8 + (1 - i)8
First let's find out the value of (1 + i)8
(1 + i)8 = [(1 + i)2]4
= (1 + i2 + 2i)4
= (2i)4
= 24 × i4
= 16 × 1 = 16 ----(1)
Similarly, let's find out the value of (1 - i)8
(1 - i)8 = [(1 - i)2]4
= [1 + i2 – 2i]4
= [1 + (-1) – 2i]4
= (-2i)4
= (-2)4 × i4
= 16 × 1 = 16 ----(2)
From equation (1) and (2)
(i + 8)
8 + (I – 8)
8 = 16 + 16 = 32