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Manipal MET2016MathematicsTrigonometric Equations

The value of _ p=1 ^6 2 ( 2 p 7 -i 2 p 7 ) is

Options

  1. A2 i
  2. B-2 i
  3. C2
  4. D1

Correct answer

A. 2 i

Step-by-step solution

Let E=-2 i _ p=1 ^6 ( 2 p 7 +i 2 p 7 ) E=-2 i _ p=1 ^6 e^ i ( 2 p 7 ) Let =e^ i ( 2 7 ) (i) array ll & E=-2 i ( + ^2+ + ^6 ) & E=-2 i [ (1+ + ^2+ + ^6 )-1 ] array E=-2 i [ ( 1- ^7 1- )-1 ] Since, ^7= (e^ i ( 2 7 ) )^7=e^ i 2 =1 E=-2 i 1- (e^ i 2 7 )^7 1-e^ i ( 2 7 ) -1 E=-2 i 1-1 1-e^ i ( 2 7 ) -1 array ll & E=-2 i(0-1) & E=2 i array

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