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The smallest positive integer n for which , is

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4
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Detailed Solution

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Concept:

  • The complex unit i is defined as .
  • i2 = -1, i3 = - i, i4 = 1 etc.
  • (a + b)2 = a2 + 2ab + b2

 

Calculation:

Given that,

    ---(1)

Let, y = 

.

∵ (a + b)2 = a2 + 2ab + b2

    (∵ i2 = -1)

Therefore, from equation (1)

The smallest positive integer for which in = 1 is n = 4.

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