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The value of (1 + i)8 + (1 - i)8 is
1. 16
2. -16
3. 32
4. -32
5. None of these

1 Answer

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Best answer
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

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