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Evaluate the expression 

  1. ei ⋅ 16π
  2. - ei ⋅ π/16
  3. ei ⋅ 8π
  4. - ei ⋅ π/8

Answer (Detailed Solution Below)

Option 1 : ei ⋅ 16π
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Detailed Solution

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Concept:

Calculation:

The given expression: can re-written as

 =  

 = 

As we know that sin π/4 = 1/√2 = cos π/4

So, we can write the given expression as

 = (cos π/4 + i sin π/4)64

As we know that, 

⇒ (cos π/4 + i sin π/4)64 = (ei ⋅ π/4 )64

⇒ (cos π/4 + i sin π/4)64 = ei ⋅ 16π

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